A Paradox

In the (albeit belated) spirit of Halloween, I shall unleash a physical trick-or-treat on my poor unsuspecting readers. Score one for American cultural imperialism. Mwahahahaha!

Now we all know that an electron and an anti-electron can annihilate each other to liberate a blinding flash of light (ok I exaggerate). Can it produce just a single photon of light? No it can't, because we can always find a frame of reference in which the electron and anti-electron have zero total momentum. But a photon knows no rest - it has non-zero momentum in any frame of reference. So this process can never occur, right? But why can't I just write down a momentum A for the electron, B for the anti-electron and C for the photon, where C = A + B? Then, at least in this frame of reference, this “reaction” can occur, right? So where's the catch?