diff --git a/include/openmc/neighbor_list.h b/include/openmc/neighbor_list.h
index f781424ff59..5b53be78d19 100644
--- a/include/openmc/neighbor_list.h
+++ b/include/openmc/neighbor_list.h
@@ -2,8 +2,9 @@
 #define OPENMC_NEIGHBOR_LIST_H
 
 #include <algorithm>
+#include <atomic>
 #include <cstdint>
-#include <forward_list>
+#include <cstdlib>
 #include <mutex>
 
 #include "openmc/openmp_interface.h"
@@ -13,51 +14,128 @@ namespace openmc {
 //==============================================================================
 //! A threadsafe, dynamic container for listing neighboring cells.
 //
-//! This container is a reduced interface for a linked list with an added OpenMP
-//! lock for write operations.  It allows for threadsafe dynamic growth; any
-//! number of threads can safely read data without locks or reference counting.
+//! This container is a reduced interface for a growable array with an added
+//! OpenMP lock for write operations. It allows for threadsafe dynamic growth;
+//! any number of threads can safely read data without locks or reference
+//! counting.
+//
+//! Entries are published through an atomic length: a writer fills the next slot
+//! and then releases the new length, and a reader acquires the length before
+//! reading any slot. That pairing is what makes the lock-free reads well
+//! defined. The first INLINE_CAPACITY entries live in the object itself, so a
+//! typical cell never allocates and a search reads the entries from the same
+//! cache line as the length. Beyond that the entries are copied into a heap
+//! block, which doubles in capacity as needed; a replaced block is retained so
+//! that a reader still traversing it stays valid, and since the capacity
+//! doubles, the retained blocks hold fewer entries than the live one.
 //==============================================================================
 
 class NeighborList {
 public:
   using value_type = int32_t;
-  using const_iterator = std::forward_list<value_type>::const_iterator;
+
+  //! Number of entries held in the object itself, before any allocation
+  static constexpr int INLINE_CAPACITY {8};
+
+  //! A snapshot of the entries that were published when it was taken
+  class View {
+  public:
+    View(const value_type* data, int size) : data_ {data}, size_ {size} {}
+    const value_type* begin() const { return data_; }
+    const value_type* end() const { return data_ + size_; }
+    int size() const { return size_; }
+
+  private:
+    const value_type* data_;
+    int size_;
+  };
+
+  NeighborList() = default;
+  NeighborList(const NeighborList&) = delete;
+  NeighborList& operator=(const NeighborList&) = delete;
+
+  ~NeighborList()
+  {
+    void* block = block_.load(std::memory_order_relaxed);
+    while (block) {
+      void* previous = *static_cast<void**>(block);
+      std::free(block);
+      block = previous;
+    }
+  }
+
+  //! Take a snapshot of the entries for lock-free traversal
+  //
+  //! The length is read first: a reader that observes a length also observes
+  //! the storage that held that many entries, since a spill to a larger block
+  //! is published before the length that counts the entry which caused it.
+  View view() const
+  {
+    int size = length_.load(std::memory_order_acquire);
+    void* block = block_.load(std::memory_order_acquire);
+    return View {block ? entries(block) : inline_, size};
+  }
 
   // Attempt to add an element.
   //
   // If the relevant OpenMP lock is currently owned by another thread, this
   // function will return without actually modifying the data.  It has been
-  // found that returning the transport calculation and possibly re-adding the
-  // element later is slightly faster than waiting on the lock to be released.
-  void push_back(int new_elem)
+  // found that returning to the transport calculation and possibly re-adding
+  // the element later is slightly faster than waiting on the lock.
+  void push_back(value_type new_elem)
   {
     // Try to acquire the lock.
     std::unique_lock<OpenMPMutex> lock(mutex_, std::try_to_lock);
-    if (lock) {
-      // It is possible another thread already added this element to the list
-      // while this thread was searching for a cell so make sure the given
-      // element isn't a duplicate before adding it.
-      if (std::find(list_.cbegin(), list_.cend(), new_elem) == list_.cend()) {
-        // Find the end of the list and add the the new element there.
-        if (!list_.empty()) {
-          auto it1 = list_.cbegin();
-          auto it2 = ++list_.cbegin();
-          while (it2 != list_.cend())
-            it1 = it2++;
-          list_.insert_after(it1, new_elem);
-        } else {
-          list_.push_front(new_elem);
-        }
-      }
-    }
-  }
+    if (!lock)
+      return;
+
+    // Only one thread writes at a time and taking the lock orders this thread
+    // against previous writers, so the entries can be read without ordering.
+    int size = length_.load(std::memory_order_relaxed);
+    void* block = block_.load(std::memory_order_relaxed);
+    value_type* data = block ? entries(block) : inline_;
+
+    // It is possible another thread already added this element to the list
+    // while this thread was searching for a cell so make sure the given
+    // element isn't a duplicate before adding it.
+    if (std::find(data, data + size, new_elem) != data + size)
+      return;
+
+    if (size == capacity_) {
+      int capacity = 2 * capacity_;
+      void* new_block =
+        std::malloc(sizeof(void*) + capacity * sizeof(value_type));
+      if (!new_block)
+        return;
 
-  const_iterator cbegin() const { return list_.cbegin(); }
+      // Chain the old block so that every block is freed on destruction, and
+      // copy the entries a reader may already be traversing.
+      *static_cast<void**>(new_block) = block;
+      value_type* new_data = entries(new_block);
+      std::copy(data, data + size, new_data);
 
-  const_iterator cend() const { return list_.cend(); }
+      block_.store(new_block, std::memory_order_release);
+      capacity_ = capacity;
+      data = new_data;
+    }
+
+    // Write the element before publishing it, so a reader that sees the new
+    // length is guaranteed to see the element too.
+    data[size] = new_elem;
+    length_.store(size + 1, std::memory_order_release);
+  }
 
 private:
-  std::forward_list<value_type> list_;
+  //! Entries follow the pointer to the previous block at the start of a block
+  static value_type* entries(void* block)
+  {
+    return reinterpret_cast<value_type*>(static_cast<void**>(block) + 1);
+  }
+
+  value_type inline_[INLINE_CAPACITY]; //!< entries before any allocation
+  std::atomic<void*> block_ {nullptr}; //!< spilled entries, chained to older
+  std::atomic<int> length_ {0};        //!< entries published in that storage
+  int capacity_ {INLINE_CAPACITY};     //!< slots in that storage; writers only
   OpenMPMutex mutex_;
 };
 
diff --git a/src/geometry.cpp b/src/geometry.cpp
index ecacf0bffbf..da328884fce 100644
--- a/src/geometry.cpp
+++ b/src/geometry.cpp
@@ -132,7 +132,9 @@ bool find_cell_inner(
   bool found = false;
   int32_t i_cell = C_NONE;
   if (neighbor_list) {
-    for (auto it = neighbor_list->cbegin(); it != neighbor_list->cend(); ++it) {
+    // Take one snapshot of the list rather than re-reading it each iteration
+    auto neighbors = neighbor_list->view();
+    for (auto it = neighbors.begin(); it != neighbors.end(); ++it) {
       i_cell = *it;
 
       // Make sure the search cell is in the same universe.