A theoretical study of the nonlinear propagation of picosecond chirped pulses in single-mode fibers is presented. We show that, under appropriate conditions, spectral narrowing-rather than broadening, as is generally believed-is induced, owing to the interplay of self-phase-modulation and dispersion. For downchirped pulses at a wavelength of 0.9 microm and a peak power as low as 0.1 W, substantial spectral narrowing occurs.