Index: src/applications/project/phid/PhabricatorProjectPHIDTypeProject.php
===================================================================
--- src/applications/project/phid/PhabricatorProjectPHIDTypeProject.php
+++ src/applications/project/phid/PhabricatorProjectPHIDTypeProject.php
@@ -42,6 +42,10 @@
       $handle->setName($name);
       $handle->setObjectName('#'.rtrim($project->getPhrictionSlug(), '/'));
       $handle->setURI("/project/view/{$id}/");
+
+      if ($project->isArchived()) {
+        $handle->setStatus(PhabricatorObjectHandleStatus::STATUS_CLOSED);
+      }
     }
   }
 
Index: src/applications/project/search/PhabricatorProjectSearchIndexer.php
===================================================================
--- src/applications/project/search/PhabricatorProjectSearchIndexer.php
+++ src/applications/project/search/PhabricatorProjectSearchIndexer.php
@@ -20,6 +20,15 @@
     $this->indexSubscribers($doc);
     $this->indexCustomFields($doc, $project);
 
+    $doc->addRelationship(
+      $project->isArchived()
+        ? PhabricatorSearchRelationship::RELATIONSHIP_CLOSED
+        : PhabricatorSearchRelationship::RELATIONSHIP_OPEN,
+      $project->getPHID(),
+      PhabricatorProjectPHIDTypeProject::TYPECONST,
+      time());
+
+
     // NOTE: This could be more full-featured, but for now we're mostly
     // interested in the side effects of indexing.