  A coloring of a matroid is proper if elements of the same color form an
independent set. For a loopless matroid M, its chromatic number \chi(M) is the
minimum number of colors that suffices to color properly the ground set E of M.
In this note we study a game-theoretic variant of this parameter proposed by
Grytczuk. Suppose that in each round of the game Alice indicates an uncolored
yet element e of E, then Bob colors it using a color from a fixed set of colors
C. The rule Bob has to obey is that it is a proper coloring. The game ends if
the whole matroid has been colored or if Bob can not color e using any color of
C. Alice wins in the first case, while Bob in the second. The minimum size of
the set of colors C for which Alice has a winning strategy is called the
indicated chromatic number of M, denoted by \chi_i(M). We prove that
\chi_i(M)=\chi(M).
