  In this paper we prove the existence of coupled K\"ahler-Einstein metrics on
complex manifolds whose canonical bundle is ample. These metrics were
introduced and their existence in the said case was proven by Hultgren and
Nystr\"om using calculus of variations. We prove the result using the method of
continuity. In the process of proving estimates, akin to the usual
K\"ahler-Einstein metrics, we reduce existence in the Fano case to a C^0
estimate.
