It would seem an old bug has resurfaced in Chrome. I am now on the latest version, 78.0.3904.108, after reinstalling Ubuntu and upgrading to 19.10, and I am now having this problem again.
When clicking the menu the first time after starting Google Chrome, the browser UI freezes for several seconds. The problem might also happen in Chromium.
The problem, if it really is the same problem, has something to do with fonts. It should have been fixed in 77.0.3865.19, but it now seems it has returned.
When I first encountered this problem, now at least a few months back, I searched intensely for a solution, finally finding a discussion on the bug tracker where someone was saying it was fixed in the next final version. At the time, this was version 77.
I remember this because I was eagerly awaiting the next stable release to fix this specific problem. Sadly, now it appears to have returned.