We consider communication over the AWGN channel with a transmitter whose battery is recharged with RF energy transfer at random times known to the receiver. We assume that the recharging process is i.i.d. Bernoulli. We characterize the capacity of this channel as the limit of an $n$-letter maximum mutual information rate under both causal and noncausal transmitter knowledge of the battery recharges. With noncausal knowledge, it is possible to explicitly identify the maximizing input distribution, which we use to demonstrate that the capacity with noncausal knowledge of the battery recharges is strictly larger than that with causal knowledge. We then proceed to derive explicit upper and lower bounds on the capacity, which are within 1.05 bits/s/Hz of each other for all parameter values.