Youtube has a couple different versions of its embeddable player (2 and 3 - which I believe correspond to the ActionScript version - AS2 or AS3). Looks like either they default to version 3 for Chrome, or they use some other way of determining a preference.
You can override this by passing &version=3 on the URL (or &version=2, depending on which layout you prefer). After mucking around trying other URL parameters, I somehow managed to make version 2 the default player for chrome (meaning I left off the “&version=3” parameter and got version 2)... but I have no idea what caused this.
You can experiment with other parameters listed here: https://developers.google.com/youtube/player_parameters#Parameters
Here’s a version 3 player, without a youtube logo, in white:
I also noticed that by specifying version=2, links with “www.youtube.com” as the domain got forwarded to “youtube.googleapis.com”, but with version=3 set, the link remained at “www.youtube.com”