The possibility of enzymatic pH oscillations is investigated for a CSTR with an outlet regulator. A linear stability analysis shows that no oscillation is possible in a CSTR without the regulator, using a proton-producing pH-dependent enzymatic reaction. However, self-sustained oscillations are found to occur in a CSTR, where the discharge of substrate is regulated at the outlet. The regions of oscillations in the parameter space are determined using a hydrolysis of N-α-benzoyl-l-arginine ethyl ester with papain. It is found that the region is quite large only when the substrate concentration in the outflow is kept at zero.