Seeing, the angular size of stellar images blurred by atmospheric turbulence, is a critical parameter used to assess the quality of astronomical sites. Median values at the best mid-latitude sites are generally in the range of 0.6--0.8,arcsec. Sites on the Antarctic plateau are characterized by comparatively-weak turbulence in the free-atmosphere above a strong but thin boundary layer. The median seeing at Dome C is estimated to be 0.23--0.36 arcsec above a boundary layer that has a typical height of 30,m. At Dome A and F, the only previous seeing measurements were made during daytime. Here we report the first direct measurements of night-time seeing at Dome A, using a Differential Image Motion Monitor. Located at a height of just 8,m, it recorded seeing as low as 0.13,arcsec, and provided seeing statistics that are comparable to those for a 20,m height at Dome C. It indicates that the boundary layer was below 8,m 31% of the time. At such times the median seeing was 0.31,arcsec, 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,m for the boundary layer at Dome A, as found from a sonic radar. The thinner boundary layer makes it less challenging to locate a telescope above it, thereby giving greater access to the free-atmosphere.