We present a confocal microscopy study of the quasi-two-dimensional crystallization of a binary mixture of spherical colloids coated with long DNA strands. Our experiments show that in the crystalline phase the two colloidal species are completely demixed. Analysis of the lattice spacings in the two types of colloidal crystal shows that the diameters of the two species of colloids differ by 10%. We argue that the demixing in the crystalline phase is due to size segregation during crystallization. This phenomenon had been predicted in several theoretical studies. To our knowledge, the present study provides the first 'real-space' experimental confirmation of this effect.