Interplanetary CubeSat missions are currently becoming more popular, with a significant number of recently planned missions. The context of this paper is a Mars mission, starting from a parking orbit around Earth: the adoption of a chemical propulsion system for the Earth-Mars transfer phase is investigated, considering the recent technological developments for CubeSats. A trade-off of propulsion system type and propellant results in the choice of a mono-propellant system adopting the HAN-based propellant AF-M315E (ASCENT). The main challenge for the propulsion system is to fit inside a CubeSat standardised volume, which can range up to 24 U, for which the implementation of a suitable COTS micro-pump is considered. Finally, the complete architecture and design of the propulsion system is presented. This work demonstrates the feasibility of adopting full chemical propulsion for an interplanetary CubeSat mission, with consequent advantages in terms of transfer time and required power, at the cost of relatively small mass and volume left for the other subsystems. Even better results can be expected for interplanetary missions requiring slightly lower AV budgets, such as Near Earth Objects exploration or asteroid fly-by missions.