In chaos-based digital communications, differential chaos-shift keying (DCSK) system has been widely studied thanks to its non-coherent demodulation without chaotic sequence synchronisation. In respect of the performance evaluation, bit error rate (BER) of the DCSK system was investigated over various transmission environments such as noise, fading, and multi-path-affected channels which are radio-propagation models from simple to complex. In this paper, the idea of applying DCSK for operation in land mobile satellite environments is proposed. A land mobile satellite channel, i.e., Lutz model with two states, is used to evaluate the system performance. Discrete-time models of transmitter and receiver over the studied channel are described. BER analysis is performed by means of Gaussian approximation and discrete integration. The analysed expressions are verified by Monte Carlo simulation. Performance comparison between different DCSK-based schemes over the studied channel is carried out. Obtained results point out that DCSK system can be used as a physical-layer modulation method using chaos for land mobile satellite applications.