The theory of vibrational ladder climbing excitation by coherent stimulated nonresonant Raman using chirped laser pulses is developed. We analytically obtain the conditions for inverting the population to a final preselected vibrational state and the restrictions that apply in the linear chirp regime. By controlling both the shape of the laser pulses and the chirp profile, the ladder climbing process can be accelerated without reducing the yield of the selective excitation. Numerical results are presented for selection of moderately excited vibrational levels in Na-2, where the important contribution of several excited electronic states is also clarified.