Injecting JS functions into the page from a Greasemonkey script on Chrome

The only way to communicate with the code running on the page in Chrome is through the DOM, so you’ll have to use a hack like inserting a <script> tag with your code. Note that this may prove buggy if your script needs to run before everything else on the page.

EDIT: Here’s how the Nice Alert extension does this:

function main () {
  // ...
  window.alert = function() {/* ... */};
  // ...
}

var script = document.createElement('script');
script.appendChild(document.createTextNode('('+ main +')();'));
(document.body || document.head || document.documentElement).appendChild(script);