Very good idea!
Try this code (not the standard code from You Tube) and validate it: (URL is only an example has nothing to do with me)
<div id="youtube">
<object type="application/x-shockwave-flash" style="width:590px; height:355px;" data="http://www.youtube.com/v/TN1rvGb30Lo?fs=1">
<param name="movie" value="http://www.youtube.com/v/TN1rvGb30Lo?fs=1" />
<param name="allowFullScreen" value="true" />
</object>
</div>