The thermal conductivity of suspended few-layer hexagonal boron nitride (h-BN) was measured using a microbridge device with built-in resistance thermometers. Based on the measured thermal resistance values of 11–12 atomic layer h-BN samples with suspended lengths ranging between 3 and 7.5 μm, the room-temperature thermal conductivity of a 11-layer sample was found to be about 360 W m–1 K–1, approaching the basal plane value reported for bulk h-BN. The presence of a polymer residue layer on the sample surface was found to decrease the thermal conductivity of a 5-layer h-BN sample to be about 250 W m–1 K–1 at 300 K. Thermal conductivities for both the 5-layer and the 11-layer samples are suppressed at low temperatures, suggesting increasing scattering of low frequency phonons in thin h-BN samples by polymer residue.