Thanks essexboy. I traced the problem to a chrome extension. Posting my experience so it might help someone else with the same symptoms:

I deleted the sync data, reset chrome, then signed in again. The problem came back, but there were a few seconds of quiet while my info was being loaded (between the time I signed in and the time the first alert sounded), which led me to believe it was one of the chrome extensions that was triggering the alert. I disabled all extensions and verified that I could surf with no alerts, and then re-enabled extensions one at a time to identify the culprit.

The chrome extension that was triggering mal:url alerts was “Orbvious Interest 1.9” (“Mark pages to read later. The fastest and most reliable Pocket (Read It Later) extension for Google Chrome”). I had used it for years with no incident so I suspect this may be an avast false positive, but I use “Save to Pocket 1.9.1” now so I had no problem getting rid of the old one.