diff --git a/Misc/NEWS b/Misc/NEWS
index 1298434..29c6214 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -13,6 +13,9 @@
 Library
 -------
 
+- Issue #23476: In the ssl module, enable OpenSSL's X509_V_FLAG_TRUSTED_FIRST
+  flag on certificate stores when it is available.
+
 - Issue #23576: Avoid stalling in SSL reads when EOF has been reached in the
   SSL layer but the underlying connection hasn't been closed.
 
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index e7ba583..a5b94eb 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -2063,6 +2063,15 @@
                                    sizeof(SID_CTX));
 #undef SID_CTX
 
+#ifdef X509_V_FLAG_TRUSTED_FIRST
+    {
+        /* Improve trust chain building when cross-signed intermediate
+           certificates are present. See https://bugs.python.org/issue23476. */
+        X509_STORE *store = SSL_CTX_get_cert_store(self->ctx);
+        X509_STORE_set_flags(store, X509_V_FLAG_TRUSTED_FIRST);
+    }
+#endif
+
     return (PyObject *)self;
 }