Nope. It was a fork of WebKit which was a fork of KHTML, the engine powering Konqueror. KHTML was developed by the KDE team.

Edit: It was widely speculated that Apple would use gecko for Safari and a shock when they announced they would use the relatively little known KHTML engine. The decision was based on KHTML having much cleaner code. I haven't looked at the Mozilla code in many years, but it was pretty gnarly back then. Lots of old cruft from the Netscape days. In comparison, KHTML was beautiful.

Ken Kocienda's book "Creative Selection: Inside Apple's Design Process During the Golden Age of Steve Jobs" has more details about the Safari team's evaluation of Mozilla code and KHTML. Ken was engineer #2 on the Safari team.

I went looking into this, and it appears that I was confused. Google was a big contributor to Firefox in the early naughties, which is the period I was thinking of. Chrome didn't come out until a good while later.

Chrome was never a fork of Firefox.

If anything, it was a fork of Konqueror.

Chrome started out as a fork of Safari, or at least WebKit.

Safari was never opensource

Yes, but WebKit was, and "Safari" might be more widely known as a name.