Why do I not have QuickTime?

For some reason, I am missing QuickTime. Whenever I go to a webpage that uses it, I get a bar on my browser that reads:

And a screen that looks like this:

When I click on the "install plugin" link, it takes me to an Apple page that tells me that my OSX system automatically has QuickTime installed. This only happens when using Chrome. But Chrome is my main browser, I don't like using Safari.

Any ideas?

Thanks in advance.