We fabricate a novel silicon-core silica-cladding optical fiber using high pressure chemical fluid deposition and investigate optical transmission characteristics at the telecommunications wavelength of 1550 nm. High thermo-optic and thermal expansion coefficients of silicon give rise to a thermal phase shift of 6.3 rad/K in a 4 mm-long, 6.9 microm diameter fiber acting as a Fabry-Perot resonator. Using both power and wavelength modulation, we observe all-optical bistability at a low threshold power of 15 mW, featuring intensity transitions of 1.4 dB occurring over <0.1 pm change in wavelength. Threshold powers for higher-order multistable states are predicted. Tristability is experimentally confirmed.