The lithosphere-asthenosphere boundary (LAB) separates rigid oceanic plates from the underlying warm ductile asthenosphere. Although a viscosity decrease beneath this boundary is essential for plate tectonics, a consensus on its origin remains elusive. Seismic studies identify a prominent velocity discontinuity at depths thought to coincide with the LAB but disagree on its cause, generally invoking either partial melting or a mantle dehydration boundary as explanations. Here we use sea-floor magnetotelluric data to image the electrical conductivity of the LAB beneath the edge of the Cocos plate at the Middle America trench offshore of Nicaragua. Underneath the resistive oceanic lithosphere, the magnetotelluric data reveal a high-conductivity layer confined to depths of 45 to 70?kilometres. Because partial melts are stable at these depths in a warm damp mantle, we interpret the conductor to be a partially molten layer capped by an impermeable frozen lid that is the base of the lithosphere. A conductivity anisotropy parallel to plate motion indicates that this melt has been sheared into flow-aligned tube-like structures. We infer that the LAB beneath young plates consists of a thin, partially molten, channel of low viscosity that acts to decouple the overlying brittle lithosphere from the deeper convecting mantle. Because this boundary layer has the potential to behave as a lubricant to plate motion, its proximity to the trench may have implications for subduction dynamics.