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

chrome/test/data/extensions/api_test/cross_origin_xhr/file_access/test.html

Index: chrome/test/data/extensions/api_test/cross_origin_xhr/file_access/test.html
diff --git a/chrome/test/data/extensions/api_test/cross_origin_xhr/file_access/test.html b/chrome/test/data/extensions/api_test/cross_origin_xhr/file_access/test.html
new file mode 100644
index 0000000000000000000000000000000000000000..2aaaab189ac94128e225508c492200466cf34e76
--- /dev/null
+++ b/chrome/test/data/extensions/api_test/cross_origin_xhr/file_access/test.html
@@ -0,0 +1,25 @@
+<script>
+chrome.test.getConfig(function(config) {
+  chrome.test.runTests([
+    function fileAccessAllowed() {
+      var req = new XMLHttpRequest();
+
+      var url = config.testDataDirectory + "/../test_file.txt";
+      chrome.test.log("Requesting url: " + url);
+      req.open("GET", url, true);
+
+      req.onload = function() {
+        chrome.test.assertEq("Hello!", req.responseText);
+        chrome.test.runNextTest();
+      }
+      req.onerror = function() {
+        chrome.test.log("status: " + req.status);
+        chrome.test.log("text: " + req.responseText);
+        chrome.test.fail("Unexpected error for url: " + url);
+      }
+
+      req.send(null);
+    }
+  ]);
+});
+</script>