An engine has a rotatable crankshaft. A compression piston is received within a compression cylinder and operatively connected to the crankshaft such that the compression piston reciprocates through an intake stroke and a compression stroke during a single rotation of the crankshaft. An expansion piston is received within an expansion cylinder and operatively connected to the crankshaft such that the expansion piston reciprocates through an expansion stroke and an exhaust stroke during a single rotation of the crankshaft. A crossover passage interconnects the compression and expansion cylinders. The crossover passage includes a crossover compression valve and a crossover expansion valve defining a pressure chamber therebetween. A fuel injector is disposed in the pressure chamber of the crossover passage. Fuel injection from the fuel injector into the crossover passage is timed to occur entirely during the compression stroke of the compression piston.