Okay, so the title is overly dramatic, but I couldn't think of anything else to call this. Not trying to actually refute relativity, those of you who know me should know this by now. This is just an interesting problem I thought up not long ago. So support we send our (very skinny) clever cosmologist away from the earth at ultra-relativistic speeds. I mean something like gamma=10^15. Our cosmologist notes that relative to his rest frame, the galaxy Andromeda is approaching with gamma=10^15. So he calculates the energy needed for this motion, gamma*mc^2, and finds it is orders of magnitude larger than the rest mass energy of the observable universe! Absurd, he concludes! In some sense, then, he thinks that he must be the one who is really in motion, for it would be impossible to impart the requisite energy to Andromeda to produce the motion he observes. Where has our poor friend gone awry?