Molecular communication requires low-complexity symbol detection algorithms to deal with the many sources of uncertainty that are inherent in these channels. This paper proposes two variants of a high-performance asynchronous peak detection algorithm for a receiver that makes independent observations. The first variant has low complexity and measures the largest observation within a sampling interval. The second variant adds decision feedback to mitigate inter-symbol interference. Although the algorithm does not require synchronization between the transmitter and receiver, results demonstrate that the bit error performance of symbol-by-symbol detection using the first variant is better than using a single sample whose sampling time is chosen a priori. The second variant is shown to have performance comparable to that of an energy detector. Both variants of the algorithm demonstrate better resilience to timing offsets than that of existing detectors.