A method is proposed for obtaining time-frequency distributions of chirp signals embedded in nonstationary noise, with the twofold objective of a sharp localization for the chirp components and a reduced level of statistical fluctuations for the noise. The technique consists in combining time-frequency reassignment with multitapering, and two variations are proposed. The first one, primarily aimed at nonstationary spectrum estimation, is based on sums of estimates with different tapers, whereas the second one makes use of differences between the same estimates for a sake of chirp enhancement. The principle of the technique is outlined, its implementation based on Hermite functions is justified and discussed, and some examples are provided for supporting the efficiency of the approach, both qualitatively and quantitatively.