When allowing an extension file:/// URL access, grant its process access to that scheme.

chrome/browser/renderer_host/chrome_render_view_host_observer.cc

Index: chrome/browser/renderer_host/chrome_render_view_host_observer.cc
diff --git a/chrome/browser/renderer_host/chrome_render_view_host_observer.cc b/chrome/browser/renderer_host/chrome_render_view_host_observer.cc
index cb924d3b6b035ffe2eaaf658f3879f7af9d0e5d0..eb0646c5bb70d713ede03186f1f1ec9001a499e8 100644
--- a/chrome/browser/renderer_host/chrome_render_view_host_observer.cc
+++ b/chrome/browser/renderer_host/chrome_render_view_host_observer.cc
@@ -116,6 +116,13 @@ void ChromeRenderViewHostObserver::InitRenderViewForExtensions() {
         process->id(), chrome::kChromeUIScheme);
   }
 
+  if (type == Extension::TYPE_EXTENSION &&
+      profile_->GetExtensionService()->extension_prefs()->AllowFileAccess(
+          extension->id())) {
+    ChildProcessSecurityPolicy::GetInstance()->GrantScheme(
+        process->id(), chrome::kFileScheme);
+  }
+
   if (type == Extension::TYPE_EXTENSION ||
       type == Extension::TYPE_USER_SCRIPT ||
       type == Extension::TYPE_PACKAGED_APP ||