diff --git a/packages/jupyter-ai/jupyter_ai/extension.py b/packages/jupyter-ai/jupyter_ai/extension.py
index a41c556c7..a9385801a 100644
--- a/packages/jupyter-ai/jupyter_ai/extension.py
+++ b/packages/jupyter-ai/jupyter_ai/extension.py
@@ -166,7 +166,7 @@ def initialize_settings(self):
         # requires the event loop to be running on init. So instead we schedule
         # this as a task that is run as soon as the loop starts, and pass
         # consumers a Future that resolves to the Dask client when awaited.
-        dask_client_future = loop.create_task(self._get_dask_client())
+        self.settings["dask_client_future"] = loop.create_task(self._get_dask_client())
 
         eps = entry_points()
         # initialize chat handlers
@@ -178,7 +178,7 @@ def initialize_settings(self):
             "root_chat_handlers": self.settings["jai_root_chat_handlers"],
             "chat_history": self.settings["chat_history"],
             "root_dir": self.serverapp.root_dir,
-            "dask_client_future": dask_client_future,
+            "dask_client_future": self.settings["dask_client_future"],
             "model_parameters": self.settings["model_parameters"],
         }
         default_chat_handler = DefaultChatHandler(**chat_handler_kwargs)
@@ -263,3 +263,27 @@ def initialize_settings(self):
 
     async def _get_dask_client(self):
         return DaskClient(processes=False, asynchronous=True)
+
+    async def stop_extension(self):
+        """
+        Public method called by Jupyter Server when the server is stopping.
+        This calls the cleanup code defined in `self._stop_exception()` inside
+        an exception handler, as the server halts if this method raises an
+        exception.
+        """
+        try:
+            await self._stop_extension()
+        except Exception as e:
+            self.log.error("Jupyter AI raised an exception while stopping:")
+            self.log.exception(e)
+
+    async def _stop_extension(self):
+        """
+        Private method that defines the cleanup code to run when the server is
+        stopping.
+        """
+        if "dask_client_future" in self.settings:
+            dask_client: DaskClient = await self.settings["dask_client_future"]
+            self.log.info("Closing Dask client.")
+            await dask_client.close()
+            self.log.debug("Closed Dask client.")
diff --git a/yarn.lock b/yarn.lock
index 3cdc4ba8b..8c398f3fd 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -15070,11 +15070,11 @@ __metadata:
 
 "typescript@patch:typescript@^3 || ^4#~builtin<compat/typescript>":
   version: 4.9.5
-  resolution: "typescript@patch:typescript@npm%3A4.9.5#~builtin<compat/typescript>::version=4.9.5&hash=23ec76"
+  resolution: "typescript@patch:typescript@npm%3A4.9.5#~builtin<compat/typescript>::version=4.9.5&hash=289587"
   bin:
     tsc: bin/tsc
     tsserver: bin/tsserver
-  checksum: ab417a2f398380c90a6cf5a5f74badd17866adf57f1165617d6a551f059c3ba0a3e4da0d147b3ac5681db9ac76a303c5876394b13b3de75fdd5b1eaa06181c9d
+  checksum: 1f8f3b6aaea19f0f67cba79057674ba580438a7db55057eb89cc06950483c5d632115c14077f6663ea76fd09fce3c190e6414bb98582ec80aa5a4eaf345d5b68
   languageName: node
   linkType: hard