diff --git a/.tsan-suppressions b/.tsan-suppressions
index 8c85014a0a..5ba86d6845 100644
--- a/.tsan-suppressions
+++ b/.tsan-suppressions
@@ -8,3 +8,9 @@
 # in practice it (hopefully!) doesn't matter.
 race:^want_color$
 race:^transfer_debug$
+
+# A boolean value, which tells whether the replace_map has been initialized or
+# not, is read racily with an update. As this variable is written to only once,
+# and it's OK if the value change right after reading it, this shouldn't be a
+# problem.
+race:^lookup_replace_object$
diff --git a/object-store.h b/object-store.h
index 55ee639350..33739c9dee 100644
--- a/object-store.h
+++ b/object-store.h
@@ -125,6 +125,8 @@ struct raw_object_store {
 	 * (see git-replace(1)).
 	 */
 	struct oidmap *replace_map;
+	unsigned replace_map_initialized : 1;
+	pthread_mutex_t replace_mutex; /* protect object replace functions */
 
 	struct commit_graph *commit_graph;
 	unsigned commit_graph_attempted : 1; /* if loading has been attempted */
diff --git a/object.c b/object.c
index 142ef69399..b4e1d3db3c 100644
--- a/object.c
+++ b/object.c
@@ -480,6 +480,7 @@ struct raw_object_store *raw_object_store_new(void)
 	memset(o, 0, sizeof(*o));
 	INIT_LIST_HEAD(&o->packed_git_mru);
 	hashmap_init(&o->pack_map, pack_map_entry_cmp, NULL, 0);
+	pthread_mutex_init(&o->replace_mutex, NULL);
 	return o;
 }
 
@@ -507,6 +508,7 @@ void raw_object_store_clear(struct raw_object_store *o)
 
 	oidmap_free(o->replace_map, 1);
 	FREE_AND_NULL(o->replace_map);
+	pthread_mutex_destroy(&o->replace_mutex);
 
 	free_commit_graph(o->commit_graph);
 	o->commit_graph = NULL;
diff --git a/replace-object.c b/replace-object.c
index e295e87943..7bd9aba6ee 100644
--- a/replace-object.c
+++ b/replace-object.c
@@ -34,14 +34,23 @@ static int register_replace_ref(struct repository *r,
 
 void prepare_replace_object(struct repository *r)
 {
-	if (r->objects->replace_map)
+	if (r->objects->replace_map_initialized)
 		return;
 
+	pthread_mutex_lock(&r->objects->replace_mutex);
+	if (r->objects->replace_map_initialized) {
+		pthread_mutex_unlock(&r->objects->replace_mutex);
+		return;
+	}
+
 	r->objects->replace_map =
 		xmalloc(sizeof(*r->objects->replace_map));
 	oidmap_init(r->objects->replace_map, 0);
 
 	for_each_replace_ref(r, register_replace_ref, NULL);
+	r->objects->replace_map_initialized = 1;
+
+	pthread_mutex_unlock(&r->objects->replace_mutex);
 }
 
 /* We allow "recursive" replacement. Only within reason, though */
diff --git a/replace-object.h b/replace-object.h
index 04ed7a85a2..3fbc32eb7b 100644
--- a/replace-object.h
+++ b/replace-object.h
@@ -24,12 +24,17 @@ const struct object_id *do_lookup_replace_object(struct repository *r,
  * name (replaced recursively, if necessary).  The return value is
  * either sha1 or a pointer to a permanently-allocated value.  When
  * object replacement is suppressed, always return sha1.
+ *
+ * Note: some thread debuggers might point a data race on the
+ * replace_map_initialized reading in this function. However, we know there's no
+ * problem in the value being updated by one thread right after another one read
+ * it here (and it should be written to only once, anyway).
  */
 static inline const struct object_id *lookup_replace_object(struct repository *r,
 							    const struct object_id *oid)
 {
 	if (!read_replace_refs ||
-	    (r->objects->replace_map &&
+	    (r->objects->replace_map_initialized &&
 	     r->objects->replace_map->map.tablesize == 0))
 		return oid;
 	return do_lookup_replace_object(r, oid);