There are many aperiodic tilings of the plane. The chromatic number of a tiling is the minimum number of colors needed to color the tiles in such a way that every pair of adjacent tiles have distinct colors. In this paper the problem is solved for the last Penrose tiling for which the problem remained unsolved, the Penrose tilings by pentacles (P 1 ). So we settle on the positive the conjecture formulated by Conway (which can be found in [2]) that Penrose tilings can be colored using only three colors. We give a such coloring for every tiling by Penrose pentacles