Chrome version 25 now supports speech recognition using the Web Speech API and Google's server-based speech recognition. 

From the W3 Web Speech API specification page:

This specification defines a JavaScript API to enable web developers to incorporate speech recognition and synthesis into their web pages. It enables developers to use scripting to generate text-to-speech output and to use speech recognition as an input for forms, continuous dictation and control. The JavaScript API allows web pages to control activation and timing and to handle results and alternatives.