In this paper, the dynamics of a discrete-time chemostat model were investigated. The discretization was obtained using the piecewise constant argument method. An analysis was performed to determine the existence and stability of fixed points. In addition, we have shown that the model experiences transcritical and period-doubling bifurcations. Two chaos control techniques, feedback control and hybrid control, were employed to control bifurcation and chaos in the model. Moreover, we provided numerical simulations to substantiate our theoretical results. This study illustrates that the piecewise constant argument method is more dynamically consistent than the forward Euler method.