This paper deals with peak to average power (PAPR) reduction in a single and multi-user 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 also presented, based on the maximum likelihood (ML) estimation of the frequency variation (up or down) of the chirp. Then, a general procedure for multi-user 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 multi-user OCDM system. Moreover, a performance analysis of the first PAPR reduction method is developed, and supported by simulation results. It is also shown that the chirp selection reduces the clipping noise, and improves the bit error rate performance compared with clipping only.