Some recent experiments, performed at Berkeley, Cologne, Florence and Vienna led to the claim that something seems to travel with a speed larger than the speed c of light in vacuum. Various other experimental results seem to point in the same direction: For instance, localized wavelet-type solutions of Maxwell equations have been found, both theoretically and experimentally, that travel with Superluminal speed. Even muonic and electronic neutrions—it has been proposed—might be “tachyons”, since their square mass appears to be negative; not to mention the apparent Superluminal expansions observed in the core of quasars and, recently, in the so-called galactic microquasars. Nevertheless, all such data or results do not place relativistic causality in jeopardy. For instance, it is possible (at least in microphysics) to solve also the known causal paradoxes, devised for “faster than light” motion, even if this is not widely recognized. Here we show, in detail and rigorously, how to solve the oldest causal paradox, originally proposed by Tolman, which is the kernel of many further tachyon paradoxes. The key to the solution is a careful application of tachyon mechanics, as it unambiguously follows from Special Relativity.