I’m not saying that it’s impossible that we’d ever find such a frame, but if we did, it would disprove Special Relativity. Which is not completely out of the question, of course: Yes, SR is the most thoroughly-tested theory in all of history, but then, that title was once held by Newtonian mechanics, too. SR would continue to be a useful approximation for anything not involving teleporters or the new physics associated with them, just as Newtonian mechanics is a useful approximation for speeds much less than c, but it would not be absolutely correct.
I avoided that problem by the simple precaution of skipping a crucial step:
I didn’t write “TraNsMogriƒier” on the side.