There is a chrome extention called Typing Speed Monitor,
This extension records how fast you type while you are actively typing. Active typing is the time you spend typing and does not include any breaks longer than 5 seconds that occur between keystrokes.
This extension will show you how fast you type when you're off doing your normal day-to-day stuff, how long you've spent typing, what characters you've typed most, and provides you with a keyboard visualization that tells you statistics about each of the keys you've typed (you mouse over keys to get more information about them). This visualization can be switched between showing you how fast you've typed certain keys to how often you've typed certain keys. Keyboard layouts supported by the visualization are QWERTY, Dvorak, and Colemak.
I found this as well as many other results by googling 'typing speed monitor'.