Early Exercise American Call

Consider an American call option with strike $K$ and maturity $T$ on a stock $S_t$ paying no dividends ($q = 0$). The risk-free rate $r > 0$ is constant.

Denote by $C_t^A$ the price of the American call and by $C_t$ the price of the corresponding European call.

Question: Is it ever optimal to exercise the American call before maturity?