I'll second KeePass. Not just because it's what I use, but because it takes serious measures to protect your data. Anyone can make a functioning password safe, but the way KeePass does it shows it was designed with an eye toward security. As a dev, I can appreciate it.
A browser extension? Really? Your OS has a massive, old, reliable security feature in that one process can not easily access the memory of another process, and you choose to not use that and instead build support directly into the largest attack vector on your PC, the browser?