mikebvm,
It depends on the solution, for free your choice will be limited. You can try an optimize any free software by compressing the libraries they ship with (if not already compressed).
Otherwise you've got premium applications that can be cloud hosted to further boost the speed/delivery. Most of these should already be optimized and will work well with both mobile and desktop based browsers.
Personally, my vote goes for Kayako's live chat software. They support many powerhouse organizations that I'm sure is heavily concerned with speed.
HTH.