  It is shown that the large $N_c$ limit of QCD with quarks in the two-index
antisymmetric color representation [QCD(AS)] has narrow tetraquark states with
exotic flavor quantum numbers. They decay into mesons with a width that is
parametrically $O(1/N_c^2)$. Tetraquarks with non-exotic quantum numbers mix at
leading order with mesons of the same overall quantum numbers. QCD(AS) at
$N_c=3$ corresponds to ordinary QCD; its large $N_c$ limit represents an
alternative starting point for a $1/N_c$ expansion to the standard one with
quarks in the fundamental color representation.
