Protocol handlers should be able to register a service worker.

chrome/browser/chrome_content_browser_client.cc

Index: chrome/browser/chrome_content_browser_client.cc
diff --git a/chrome/browser/chrome_content_browser_client.cc b/chrome/browser/chrome_content_browser_client.cc
index 0f9113561b6b3e947b78bc6421dd00819f02bfbe..479ffecb81442ca2af59b72b420cf1d872ab87bd 100644
--- a/chrome/browser/chrome_content_browser_client.cc
+++ b/chrome/browser/chrome_content_browser_client.cc
@@ -35,6 +35,7 @@
 #include "chrome/browser/chrome_quota_permission_context.h"
 #include "chrome/browser/content_settings/cookie_settings_factory.h"
 #include "chrome/browser/content_settings/tab_specific_content_settings.h"
+#include "chrome/browser/custom_handlers/protocol_handler_registry_factory.h"
 #include "chrome/browser/defaults.h"
 #include "chrome/browser/devtools/chrome_devtools_manager_delegate.h"
 #include "chrome/browser/download/download_prefs.h"
@@ -1006,6 +1007,13 @@ bool ChromeContentBrowserClient::IsHandledURL(const GURL& url) {
   return ProfileIOData::IsHandledURL(url);
 }
 
+GURL ChromeContentBrowserClient::GetHandlerFor(
+    content::BrowserContext* browser_context, const GURL& url) {
+  ProtocolHandlerRegistry* registry =
+      ProtocolHandlerRegistryFactory::GetForBrowserContext(browser_context);
+  return registry->GetHandlerFor(url.scheme()).TranslateUrl(url);
+}
+
 bool ChromeContentBrowserClient::CanCommitURL(
     content::RenderProcessHost* process_host,
     const GURL& url) {