We extend a previously developed one dimensional causal theory of tachyons to three dimensions. The result is a three dimensional theory of interacting tachyons in which coordinates in reference frames with sub‐luminal relative velocity are related by the Lorentz transformations, and in which no paradoxes involving causal loops can arise. The resulting theory involves a preferred spatial direction and preferred velocity perpendicular to that direction, so that physical laws governing tachyons are not invariant under rotations or proper Lorentz transformations. This lack of invariance should manifest itself even in processes involving only bradyons, to the extent that coupling to virtual tachyons is important. We discuss the limits which experimental evidence on the validity of rotational invariance places on tachyon couplings in the theory and possible additional experiments for searching for lack of such invariance.