After reinstalling Mac OS Sierra, I found that Chrome could no longer use my HTTPS client certificates. Instead, after choosing my certificate from Chrome’s pop-up certificate picking menu, I just got a fatal “ERR_SSL_CLIENT_AUTH_SIGNATURE_FAILED” error. The HTTPS client certificates worked fine in Safari, so it seemed to be a Chrome-specific problem.
I was able to fix this by opening the Keychain Access program, right-clicking my HTTPS private key and selecting Get Info, then on the Access Control tab I changed it from “allow all applications to use this item” to “confirm before allowing access”. The next time I tried to view the website in Chrome, Mac OS popped up to confirm that I wanted to allow it to use the key, and it worked perfectly after clicking Allow! I guess the Keychain’s application permissions got messed up at some point, and this reset it.