diff --git a/lib/vtls/openssl.c b/lib/vtls/openssl.c
index 6378e10ff..1df32558b 100644
--- a/lib/vtls/openssl.c
+++ b/lib/vtls/openssl.c
@@ -2013,6 +2013,20 @@ static CURLcode ossl_connect_step1(struct connectdata *conn, int sockindex)
           data->set.str[STRING_SSL_CRLFILE]: "none");
   }
 
+  /* Try building a chain using issuers in the trusted store first to avoid
+  problems with server-sent legacy intermediates.
+  Newer versions of OpenSSL do alternate chain checking by default which
+  gives us the same fix without as much of a performance hit (slight), so we
+  prefer that if available.
+  https://rt.openssl.org/Ticket/Display.html?id=3621&user=guest&pass=guest
+  */
+#if defined(X509_V_FLAG_TRUSTED_FIRST) && !defined(X509_V_FLAG_NO_ALT_CHAINS)
+  if(data->set.ssl.verifypeer) {
+    X509_STORE_set_flags(SSL_CTX_get_cert_store(connssl->ctx),
+                         X509_V_FLAG_TRUSTED_FIRST);
+  }
+#endif
+
   /* SSL always tries to verify the peer, this only says whether it should
    * fail to connect if the verification fails, or if it should continue
    * anyway. In the latter case the result of the verification is checked with