We present the first demonstration of frequency conversion by simultaneous second- and third-harmonic generation in a silicon photonic crystal nanocavity using continuous-wave optical excitation. We observe a bright dual wavelength emission in the blue/green (450-525 nm) and red (675-790 nm) visible windows with pump powers as low as few microwatts in the telecom bands, with conversion efficiencies of ∼ 10 (-5) /W and ∼ 10/ W(2) for the second- and third-harmonic, respectively. Scaling behaviors as a function of pump power and cavity quality-factor are demonstrated for both second- and third order processes. Successful comparison of measured and calculated emission patterns indicates that third-harmonic is a bulk effect while second-harmonic is a surface-related effect at the sidewall holes boundaries. Our results are promising for obtaining practical low-power, continuous-wave and widely tunable multiple harmonic generation on a silicon chip.