This paper studies power allocation for Chase combining (CC) hybrid ARQ (HARQ) in block-fading channels, with causal channel state information (CSI) available both at the receiver and transmitter. A best-effort power allocation scheme is proposed to improve the average throughput of CC HARQ. The scheme is formulated as an optimization problem that, for each round, allocating the transmit power to maximize the average incremental information according to the HARQ retransmission status and CSI. By convex optimization, the solution is derived in simple analytical form. At the same time, the HARQ performance metrics including throughput and outage probability are computed by recursive numerical integral. With at most 4 transmission rounds, this best-effort method achieves about 75% of ergodic capacity in independent Rayleigh block fading channels.