In this paper, we consider an energy harvesting multiple access channel (MAC) where the transmitters are powered by energy harvested from the ambient environment. We assume that the energy harvesting processes at the transmitters can be modeled as independent Bernoulli processes with parameters λis, and the channel states between the transmitters and the receiver are independent Bernoulli processes with parameter μis. An active transmitter always transmits with a fixed power and consumes one unit amount of energy in a time slot. Under the assumption that μi ≥ λi, Ai, our objective is to schedule the transmissions adaptively according to the instantaneous channel and battery states of transmitters, so that the long-term average sum-throughput of the MAC is maximized in expectation. We first show that for a general asymmetric scenario where λis and μis are not identical across the transmitters, the expected long-term average sum-throughput has an upper bound for any transmission scheduling policy satisfying the energy causality constraints. We then consider a special symmetric scenario where λis and μis are uniform among transmitters. We propose a randomized longest-connected-queue transmission scheduling policy and show that it achieves the upper bound almost surely as time T approaches infinity, thus it is optimal.