The tunnelling of a particle through a barrier is one of the most fundamental and ubiquitous quantum processes. When induced by an intense laser field, electron tunnelling from atoms and molecules initiates a broad range of phenomena such as the generation of attosecond pulses(1), laser-induced electron diffraction(2,3) and holography(2,4). These processes evolve on the attosecond timescale (1 attosecond equivalent to 1 as = 10(-18) seconds) and are well suited to the investigation of a general issue much debated since the early days of quantum mechanics(5-7)-the link between the tunnelling of an electron through a barrier and its dynamics outside the barrier. Previous experiments have measured tunnelling rates with attosecond time resolution(8) and tunnelling delay times(9). Here we study laser-induced tunnelling by using a weak probe field to steer the tunnelled electron in the lateral direction and then monitor the effect on the attosecond light bursts emitted when the liberated electron re-encounters the parent ion(10). We show that this approach allows us to measure the time at which the electron exits from the tunnelling barrier. We demonstrate the high sensitivity of the measurement by detecting subtle delays in ionization times from two orbitals of a carbon dioxide molecule. Measurement of the tunnelling process is essential for all attosecond experiments where strong-field ionization initiates ultrafast dynamics(10). Our approach provides a general tool for time-resolving multi-electron rearrangements in atoms and molecules(11-13)-one of the key challenges in ultrafast science.