Biocompatible solid electrolyte chitosan is introduced as a protonic/electronic electric double layer (EDL) dielectric in a multilayer MoS2 transistor. This chitosan‐bioinspired transistor can operate at a low working voltage (<3 V) and exhibits an asymmetric ambipolar behavior. A high on/off ratio (∼104) was achieved for both electrons and holes, in conjunction with a very steep subthreshold swing (67 mV/dec) which is close to the theoretical limit of an ideal field‐effect transistor (60 mV/dec). It was established that the on‐state conductance of these devices is strongly limited by the contact resistance of the metal–MoS2 junctions, and the conductance can be increased by a factor of ∼3 by using dual‐gate electrostatic modulation. Further exploiting the double‐gate geometry allows us to characterize the contact resistance in the on‐regime. We make a numerical simulation and observe important contributions that are independently modulated by back and top gates stemming from Schottky barriers formed at the MoS2/metal interface and the chitosan‐induced charge accumulation near the electrode, respectively. Such EDL multilayer MoS2 transistors with bioinspired chitosan solid electrolyte can provide a new opportunity for the fabrication of low voltage and cost‐effective two‐dimensional semiconductor devices which are also biocompatible and environment friendly.