diff --git a/CHANGES/5259.bugfix b/CHANGES/5259.bugfix
new file mode 100644
index 00000000000..c53e99e0825
--- /dev/null
+++ b/CHANGES/5259.bugfix
@@ -0,0 +1 @@
+Acquire the connection before running traces to prevent race condition.
diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index 52f97c75f5a..5eea16aa6c1 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -48,6 +48,7 @@ Arthur Darcet
 Ben Bader
 Ben Timby
 Benedikt Reinartz
+Bob Haddleton
 Boris Feld
 Boyi Chen
 Brett Cannon
diff --git a/aiohttp/connector.py b/aiohttp/connector.py
index 93b07490327..e6c36fba0d8 100644
--- a/aiohttp/connector.py
+++ b/aiohttp/connector.py
@@ -553,8 +553,14 @@ async def connect(
                     await trace.send_connection_create_end()
         else:
             if traces:
+                # Acquire the connection to prevent race conditions with limits
+                placeholder = cast(ResponseHandler, _TransportPlaceholder())
+                self._acquired.add(placeholder)
+                self._acquired_per_host[key].add(placeholder)
                 for trace in traces:
                     await trace.send_connection_reuseconn()
+                self._acquired.remove(placeholder)
+                self._drop_acquired_per_host(key, placeholder)
 
         self._acquired.add(proto)
         self._acquired_per_host[key].add(proto)