Chrome asks for my keyring, but no other browser does, including Rekonq and
Konqueror which are part of KDE. I have every possible browser installed.
However, once the Wallet password is entered you do not need to enter it
again. You can turn that off in the KDE Wallet settings. It may not be a
browser thing, but that is the default setting for Chrome or Chromium for
some reason. Also Choqok and a few other applications to do the same thing.