From some quick searching, apparently it's closed-source, but built on top of Chromium's rendering engine (Blink).
Chrome is of course mostly open source, except for some proprietary bits. The same is basically true of Vivaldi (and Opera), they all add a relatively small amount of proprietary code on top of the massive open source Chromium codebase.
* Preinstalled proprietary plugins (Widevine, Flash) * More preinstalled codecs (woohoo, patents!) * Various user metrics reporting
There is a pretty big difference between that and keeping all of your changes private.
Also, Opera has been contributing to Blink, so they aren't keeping all their changes private.
Vivaldi hasn't launched yet, but I would guess the same would be true of them - it just isn't rational to do otherwise (if Vivaldi fixes some small bug in Blink, why keep it as a patch they need to constantly reapply on top of Blink? Far easier to upstream it).
So aside from the UI (which is tiny compared to the entire browser), Chrome, Blink and Vivaldi are about equal in terms of being open or closed.
I was a pretty die-hard Opera fan for many years, so this news really piqued my interest... up until I learned the software is not libre.