We report signal amplification by 1/f(alpha) noise with stochastic resonance in a nonlinear nanomechanical resonator. The addition of 1/f(alpha) noise to a subthreshold modulation signal enhances the probability of an electrostatically driven resonator switching between its two vibrational states in the hysteretic region. Considering the prevalence of 1/f noise in the materials in integrated circuits, signal enhancement demonstrated here, using a fully on-chip electronic actuation/detection scheme, suggests beneficial use of the otherwise detrimental noise.