Enable sync for the settings from the Extension Settings API.

chrome/browser/sync/profile_sync_service.cc

Index: chrome/browser/sync/profile_sync_service.cc
diff --git a/chrome/browser/sync/profile_sync_service.cc b/chrome/browser/sync/profile_sync_service.cc
index 334b08cdd729ba50418fd8ad53b9f409d36635cb..d6534a9c0276b879f8dbb1a53cb2926e2f3a9ef8 100644
--- a/chrome/browser/sync/profile_sync_service.cc
+++ b/chrome/browser/sync/profile_sync_service.cc
@@ -312,6 +312,9 @@ void ProfileSyncService::RegisterPreferences() {
   pref_service->RegisterBooleanPref(prefs::kSyncTypedUrls,
                                     enable_by_default,
                                     PrefService::UNSYNCABLE_PREF);
+  pref_service->RegisterBooleanPref(prefs::kSyncExtensionSettings,
+                                    enable_by_default,
+                                    PrefService::UNSYNCABLE_PREF);
   pref_service->RegisterBooleanPref(prefs::kSyncExtensions,
                                     enable_by_default,
                                     PrefService::UNSYNCABLE_PREF);
@@ -563,6 +566,8 @@ const char* ProfileSyncService::GetPrefNameForDataType(
       return prefs::kSyncThemes;
     case syncable::TYPED_URLS:
       return prefs::kSyncTypedUrls;
+    case syncable::EXTENSION_SETTINGS:
+      return prefs::kSyncExtensionSettings;
     case syncable::EXTENSIONS:
       return prefs::kSyncExtensions;
     case syncable::APPS: