We investigate swimming and chemotactic behaviors of the polarly flagellated marine bacteria Vibrio alginolyticus in an aqueous medium. Our observations show that V. alginolyticus execute a cyclic, three-step (forward, reverse, and flick) swimming pattern that is distinctively different from the run-tumble pattern adopted by Escherichia coli. Specifically, the bacterium backtracks its forward swimming path when the motor reverses. However, upon resuming forward swimming, the flagellum flicks and a new swimming direction is selected at random. In a chemically homogeneous medium (no attractant or repellent), the consecutive forward t(f) and backward t(b) swimming times are uncorrelated. Interestingly, although t(f) and t(b) are not distributed in a Poissonian fashion, their difference Δt = |t(f) - t(b)| is. Near a point source of attractant, on the other hand, t(f) and t(b) are found to be strongly correlated, and Δt obeys a bimodal distribution. These observations indicate that V. alginolyticus exploit the time-reversal symmetry of forward and backward swimming by using the time difference to regulate their chemotactic behavior. By adopting the three-step cycle, cells of V. alginolyticus are able to quickly respond to a chemical gradient as well as to localize near a point source of attractant.