Seeing-the angular size of stellar images blurred by atmospheric turbulence-is a critical parameter used to assess the quality of astronomical sites at optical/infrared wavelengths. Median values at the best mid-latitude sites are generally in the range of 0.6-0.8 arcseconds1-3. Sites on the Antarctic plateau are characterized by comparatively weak turbulence in the free atmosphere above a strong but thin boundary layer4-6. The median seeing at Dome C is estimated to be 0.23-0.36 arcseconds7-10 above a boundary layer that has a typical height of 30 metres10-12. At Domes A and F, the only previous seeing measurements have been made during daytime13,14. Here we report measurements of night-time seeing at Dome A, using a differential image motion monitor15. Located at a height of just 8 metres, it recorded seeing as low as 0.13 arcseconds, and provided seeing statistics that are comparable to those at a height of 20 metres at Dome C. This indicates that the boundary layer was below 8 metres for 31 per cent of the time, with median seeing of 0.31 arcseconds, consistent with free-atmosphere seeing. The seeing and boundary-layer thickness are found to be strongly correlated with the near-surface temperature gradient. The correlation confirms a median thickness of approximately 14 metres for the boundary layer at Dome A, as found from a sonic radar16. The thinner boundary layer makes it less challenging to locate a telescope above it, thereby giving greater access to the free atmosphere.