A split-cycle engine includes: a first cylinder housing a first piston, wherein the first piston performs an intake stroke and a compression stroke, but does not perform an exhaust stroke; a second cylinder housing a second piston, wherein the second piston performs an expansion stroke and an exhaust stroke, but does not perform an intake stroke; and a valve chamber housing a valve, the valve comprising an internal chamber that selectively fluidly couples to the first and second cylinders, wherein the valve and internal chamber move within the valve chamber and relative to the first and second cylinders.