The density of GABA_A receptors (GABA_ARs) at synapses regulates brain excitability, and altered inhibition may contribute to Huntington's disease, which is caused by a polyglutamine repeat in the protein huntingtin. However, the machinery that delivers GABA_ARs to synapses is unknown. We demonstrate that GABA_ARs are trafficked to synapses by the kinesin family motor protein 5 (KIF5). We identify the adaptor linking the receptors to KIF5 as the huntingtin-associated protein 1 (HAP1). Disrupting the HAP1-KIF5 complex decreases synaptic GABA_AR number and reduces the amplitude of inhibitory postsynaptic currents. When huntingtin is mutated, as in Huntington's disease, GABA_AR transport and inhibitory synaptic currents are reduced. Thus, HAP1-KIF5-dependent GABA_AR trafficking is a fundamental mechanism controlling the strength of synaptic inhibition in the brain. Its disruption by mutant huntingtin may explain some of the defects in brain information processing occurring in Huntington's disease and provides a molecular target for therapeutic approaches.