If you strictly need Google Chrome and accept the security risks for offline or basic testing, you can fetch the legacy installer.
Mountain Lion was a beautiful, stable operating system. It represents an era when Macs felt like precision instruments. But the web moves forward, and so must we. Chrome for Mac OS X 10.8.5 exists as a museum piece—interesting to look at, but dangerous to live in. chrome for mac os x 10.8.5