Voltage-dependent K+ (Kv) channels repolarize the action potential in neurons and muscle. This type of channel is gated directly by membrane voltage through protein domains known as voltage sensors, which are molecular voltmeters that read the membrane voltage and regulate the pore. Here we describe the structure of a chimaeric voltage-dependent K+ channel, which we call the `paddle-chimaera channel', in which the voltage-sensor paddle has been transferred from Kv2.1 to Kv1.2. Crystallized in complex with lipids, the complete structure at 2.4ångström resolution reveals the pore and voltage sensors embedded in a membrane-like arrangement of lipid molecules. The detailed structure, which can be compared directly to a large body of functional data, explains charge stabilization within the membrane and suggests a mechanism for voltage-sensor movements and pore gating.