We have performed molecular dynamics simulations and developed a scaling model of a nanopropulsion engine. The engine consists of a nozzlelike pore with catalytic sites located at the closed end of the nozzle. The nozzle is immersed in a solution of monomers that serves as a "fuel" for the polymerization reaction. The engine can be thought of as an analogue of the jet propulsion engine that secretes polymers in a solution and utilizes polymer viscoelasticity for its motion. Using scaling analysis, we have established that the nozzle velocity is proportional to the chain's polymerization rate with the proportionality coefficient being determined by the nozzle geometry, the nozzle friction coefficient, and the dynamics of the polymer chains inside the nozzle. The results of the molecular dynamics simulations are in remarkable agreement with the predictions of the scaling model.