This paper deals with peak to average power (PAPR) reduction in a single and multiuser orthogonal chirp division multiplexing (OCDM) context. Two methods for PAPR reduction based on the selection of the frequency variation (up or down) of the chirps are first presented in a single user system. The first technique consists in considering two OCDM signals generated with up and down chirps, respectively, and selecting the one offering lowest PAPR. The second PAPR reduction method is based on usual clipping, and in that case the chirp selection aims to reduce the clipping noise. An adapted receiver is presented, based on the maximum likelihood (ML) estimation of the frequency variation (up or down) of the chirp. Then, a general procedure for multiuser OCDM transmission is introduced, where a sub-band of the available bandwidth is dedicated to each user, whose frequency of the chirps varies within this sub-band. Next, the PAPR reduction techniques are generalized to this multiuser OCDM system. Moreover, a performance analysis of the first PAPR reduction method is developed, and it is shown through simulations that theoretical and numerical results match for both Nyquist rate and oversampled signals. It is also shown that the chirp selection reduces the clipping noise, and improves the bit error rate (BER) performance compared with clipping only.