diff --git a/jaxtyping/decorator.py b/jaxtyping/decorator.py
index 3099007..68ceb0c 100644
--- a/jaxtyping/decorator.py
+++ b/jaxtyping/decorator.py
@@ -22,16 +22,19 @@ import threading
 
 
 storage = threading.local()
-storage.memo_stack = []
 
 
 def jaxtyped(fn):
     @ft.wraps(fn)
     def wrapper(*args, **kwargs):
-        storage.memo_stack.append(({}, {}, {}))
+        try:
+            memo_stack = storage.memo_stack
+        except AttributeError:
+            memo_stack = storage.memo_stack = []
+        memo_stack.append(({}, {}, {}))
         try:
             return fn(*args, **kwargs)
         finally:
-            storage.memo_stack.pop()
+            memo_stack.pop()
 
     return wrapper
diff --git a/test/test_threading.py b/test/test_threading.py
new file mode 100644
index 0000000..24c50b3
--- /dev/null
+++ b/test/test_threading.py
@@ -0,0 +1,41 @@
+# Copyright (c) 2022 Google LLC
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy of
+# this software and associated documentation files (the "Software"), to deal in
+# the Software without restriction, including without limitation the rights to
+# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+# the Software, and to permit persons to whom the Software is furnished to do so,
+# subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
+# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
+# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+import threading
+
+import jax.numpy as jnp
+from typeguard import typechecked
+
+from jaxtyping import Array, Float, jaxtyped
+
+
+def test_threading():
+    @jaxtyped
+    @typechecked
+    def add(x: Float[Array, "a b"], y: Float[Array, "a b"]) -> Float[Array, "a b"]:
+        return x + y
+
+    def run():
+        a = jnp.array([[1.0, 2.0]])
+        b = jnp.array([[2.0, 3.0]])
+        add(a, b)
+
+    thread = threading.Thread(target=run)
+    thread.start()
+    thread.join()