This is proved in §B.6 as the dual of the shift-theorem. It is also evident from inspection of the Fourier transform:
Applying the modulation theorem to the Gaussian transform pair above yields
Thus, we frequency-shift a Gaussian chirp in the same way we frequency-shift any signal--by complex modulation (multiplication by a complex sinusoid at the shift-frequency).
Identifying Chirp Rate
Chirplet Fourier Transform