Multiband supercontinuum generation covering the bandwidth from 0.65 μm to 3.3 μm was demonstrated in a gas-filled hollow-core silica fiber pumped by chirped ultrashort pulses at 1.03 μm. The development of the SC spectrum into the mid-IR was initiated by cascade stimulated Raman scattering in gaseous D2, which was used as an active medium filling the hollow core. The influence of the Kerr nonlinearity was studied by changing the linear chirp of the pump pulses. The influence of gas pressure and pump pulse energy on the SC generation was investigated. As high as 14% of pump quanta were converted to the wavelength range above 2 μm.