The advent of two-dimensional materials has opened a plethora of opportunities in accessing ultrascaled device dimensions for future logic and memory applications. In this work, we demonstrate that a single layer of large-area chemical vapor deposition-grown molybdenum disulfide (MoS2) sandwiched between two metal electrodes can be tuned to show multilevel nonvolatile resistive memory states with resistance values separated by 5 orders of magnitude. The switching process is unipolar and thermochemically driven requiring significant Joule heating in the reset process. Temperature-dependent electrical measurements coupled with semiclassical charge transport models suggest that the transport in these devices varies significantly in the initial (pristine) state, high resistance state, and low resistance state. In the initial state, the transport is a one-step direct tunneling (at low voltage biases) and Fowler Nordeim tunneling (at higher bias) with an effective barrier height of 0.33 eV, which closely matches the Schottky barrier at the MoS2/Au interface. In the high resistive state, trap-assisted tunneling provides a reasonable fit to experimental data for a trap height of 0.82 eV. Density functional theory calculations suggest the possibility of single- and double-sulfur vacancies as the microscopic origins of these trap sites. The temperature-dependent behavior of the set and reset process are explained by invoking the probability of defect (sulfur vacancy) creation and mobility of sulfur ions. Finally, conductive atomic force microscopy measurements confirm that the multifilamentary resistive memory effects are inherent to a single-crystalline MoS2 triangle and not necessarily dependent on grain boundaries. The insights suggested in this work are envisioned to open up possibilities for ultrascaled, multistate, resistive memories for next-generation digital memory and neuromorphic applications.