diff --git a/Lib/_threading_local.py b/Lib/_threading_local.py
index 6d77035..6e8a8d8 100644
--- a/Lib/_threading_local.py
+++ b/Lib/_threading_local.py
@@ -217,10 +217,12 @@
         key = object.__getattribute__(self, '_local__key')
 
         try:
-            threads = list(threading.enumerate())
+            # We use the non-locking API since we might already hold the lock
+            # (__del__ can be called at any point by the cyclic GC).
+            threads = threading._enumerate()
         except:
-            # If enumerate fails, as it seems to do during
-            # shutdown, we'll skip cleanup under the assumption
+            # If enumerating the current threads fails, as it seems to do
+            # during shutdown, we'll skip cleanup under the assumption
             # that there is nothing to clean up.
             return
 
diff --git a/Lib/threading.py b/Lib/threading.py
index 88101b0..d5412e9 100644
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -798,6 +798,10 @@
 
 activeCount = active_count
 
+def _enumerate():
+    # Same as enumerate(), but without the lock. Internal use only.
+    return list(_active.values()) + list(_limbo.values())
+
 def enumerate():
     with _active_limbo_lock:
         return list(_active.values()) + list(_limbo.values())
diff --git a/Misc/NEWS b/Misc/NEWS
index c67407f..2ce6070 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -40,6 +40,9 @@
 Library
 -------
 
+- Issue #7264: Fix a possible deadlock when deallocating thread-local objects
+  which are part of a reference cycle.
+
 - Issue #6896: mailbox.Maildir now invalidates its internal cache each time
   a modification is done through it.  This fixes inconsistencies and test
   failures on systems with slightly bogus mtime behaviour.