It's possible that you have the wrong inner tube in the tire. the wrong inner tube woudl allow too much room between the tire and the rim. as speed increases your tires will "grow" taller. if the inner tube is too small it will not help hold the tire to the rim, that could be why it's coming off. or the bead of the tire is too worn and it is not seating into the rim far enough. again, at high speeds the tires grow taller and stretch a little.
I don;t think a chain issue is the problem, unless your chain is binding and causing the rear wheel to lock up.
But really, if the tire is coming off the rim, i would get a new tire and a new inner tube...i think it's a tire/inner tube /rim issue myself.
with the correct inner tube, air pressure and a tire with a good bead, it would be VERY difficult for the tire to come off the rim. i have never heard of this happening before.
or, possibly the rim where the bead of the tire goes is messed up? not allowing the bead of the tire to stay seated? i don't know, i'm baffled on this one.