Why does chrome open and immediately redirect to an ad site?

Booting the phone up in safe mode stops it, and I can't figure out what is causing it.

That's a clear sign that the culprit is an app that you downloaded. You have to narrow the search trying to remember when this issue started and which apps where installed, or updated, at that point. The usual suspects could be free games, memory or battery boosters, etc.

You could try clearing cache and data for Chrome in settings - apps and see if this makes a difference.