Time and frequency dependences of coherent anti‐Stokes Raman scattering (CARS) are here found analytically for the increasingly popular experimental approach where the Raman preparation and probing are realized by means of very short linearly chirped laser pulses. These are chosen with Gaussian lineshapes that, besides being rather common in ultrashort laser physics, guarantee full solution to the nonlinear scattering problem at hand. The solution appears rather simple in spite of the complications arising from the treatment of optical nonlinearities of different nature (dielectric susceptibility of the third order for the Raman medium and quadratic phases of three laser fields). The simplicity of the solution allows versatile applications that are here shown for different chirp effects in vibrational and purely rotational N2 CARS whose spectral complexity provides an excellent ground to test the model. The comparison with known experiments shows a good agreement except for some limitations imposed by deviations of the nonresonant CARS signal from the Gaussian structure assumed in the model.