The Zintl compound CaAl2Si2 peritectically decomposes to a new ternary cubic Laves phase Ca(Al,Si)(2) and an Al Si eutectic at temperatures above 750 degrees C under a pressure of 13 GPa. The ternary Laves phase compound can also be prepared as solid solutions Ca(Al1-xSix)(2) (0.35 <= x <= 0.75) directly from the ternary mixtures under high-pressure and high-temperature conditions. The cubic Laves phase structure can be regarded as a type of clathrate compound composed of face-sharing truncated tetrahedral cages with Ca atoms at the center, Ca@(Al,Si)(2). The compound with a stoichiometric composition CaAlSi exhibits superconductivity with a transition temperature of 2.6 K. This is the first superconducting Laves phase compound composed solely of commonly found elements.