Tunnelling is one of the most characteristic phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from superconducting quantum interference device (SQUID) magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel through a barrier, however, has remained contentious since the first attempts to calculate it(1). It is now well understood that the group delay(2)-the arrival time of the peak of the transmitted wavepacket at the far side of the barrier-can be smaller than the barrier thickness divided by the speed of light, without violating causality. This has been confirmed by many experiments(3-6), and a recent work even claims that tunnelling may take no time at all(7). There have also been efforts to identify a different timescale that would better describe how long a given particle spends in the barrier region(8-10). Here we directly measure such a time by studying Bose-condensed(87)Rb atoms tunnelling through a 1.3-micrometre-thick optical barrier. By localizing a pseudo-magnetic field inside the barrier, we use the spin precession of the atoms as a clock to measure the time that they require to cross the classically forbidden region. We study the dependence of the traversal time on the incident energy, finding a value of 0.61(7) milliseconds at the lowest energy for which tunnelling is observable. This experiment lays the groundwork for addressing fundamental questions about history in quantum mechanics: for instance, what we can learn about where a particle was at earlier times by observing where it is now(11-13). Using the spin precession of Bose-condensed(87)Rb atoms as a clock, direct measurements are made of the time required for Rb atoms to quantum tunnel through a classically impenetrable barrier.