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Here's an article on how to detect chrome:
http://javascriptly.com/2008/09/javascript-to-detect-google-chrome/
And this question: Disable tab key on a specific div might help you on disabling the tab key. If you are able to combine both yourself, you've probably got it working.
The disable function would become something like:
$('.textarea').on('keyup mouseup', function(e) {
if(e.which == 9) { e.preventDefault(); }
});
e.which = 9 is the tab key according to the last link given. If you are able to wrap the browser detection around it yourself, I guess you've got your working example.