We carry out a detailed analysis of the OPE of two N=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N=2 SCFTs, imply an analytic lower bound on the central charge c. The bound is valid for any N=2 SCFT regardless of its matter content and flavor symmetries. Browsing the N=2 literature, we find that our bound is saturated by the simplest Argyres-Douglas fixed point.