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This thesis presents a preliminary design of an ionospheric sounder to be carried aboard one or more of NASA's Mars Surveyor landers. Past Russian and American probes have indicated the existence of an ionosphere, but none of these missions remotely sensed this atmospheric layer from the surface. The rationale for utilizing a surface-based Martian ionospheric sounder is discussed. Based on NASA's choice of launch vehicle and power source, a low-weight, low-powered Chirp sounder using a horizontally-polarized dipole antenna is recommended for the sounder experiment. The sounder experiment should be conducted for at least one Martian year, in order to investigate significant changes in radio propagation during seasonal transitions. Specific data compression techniques are suggested in order to reduce the quantity of data transferred from each sounder. The Appendix presents an overview of Earth's ionospheric structure and solar cycle effects. Finally, a Matlab software model of a hypothetical ionogram as measured from the Martian surface is presented.