NEXT-100 is an electroluminescent high-pressure xenon gas time projection chamber that will search for the neutrinoless double beta (0νββ) decay of 136Xe. The detector possesses two features of great value for 0νββ searches: energy resolution better than 1% FWHM at the Q value of 136Xe and track reconstruction for the discrimination of signal and background events. This combination results in excellent sensitivity, as discussed in this paper. Material-screening measurements and a detailed Monte Carlo detector simulation predict a background rate for NEXT-100 of at most 4 × 10−4 counts keV−1 kg−1 yr−1. Accordingly, the detector will reach a sensitivity to the 0νββ-decay half-life of 2.8 × 1025 years (90% CL) for an exposure of 100 kg·year, or 6.0 × 1025 years after a run of 3 effective years.