We investigate the propagation dynamics of nonlinear chirped optical laser pulses in a two-level medium. For certain chirp strength and chirp width, an incident 2π nonlinear chirped pulse will split into optical precursors and a stable self-induced transparency soliton. This is caused by the particular Fourier spectrum that includes not only central resonant frequency components but also high-frequency and low-frequency sidebands. Moreover, the effects of chirp parameters on the evolution of nonlinear chirped pulses are also discussed.