Of the approaches currently under investigation for the fabrication of functional III-V semiconductor nanostructures, self-organized growth mechanisms and directed growth on patterned substrates have yielded quantum wires and dots with the best structural and electronic properties . In patterned growth, high densities of structures are difficult to obtain; self-organization, on the other hand, can provide densely packed structures with good crystal quality, but generally offers limited control over nanostructure uniformity and spatial position. In the case of quantum dots, non-uniformity of size and shape is clearly undesirable, as the resulting structures will exhibit a broad range of electronic and optical properties, effectively smearing out the sought-for zero-dimensional behaviour of the dot ensemble. Here we demonstrate a method for improving size uniformity, while maintaining a high density of quantum dots, that combines elements of both self-organization and patterning. The photoluminescence spectrum of the resulting ordered arrays of quantum dots is dominated by a single sharp line, rather than the series of sharp lines that would indicate transitions in quantum dots of different sizes [2-7].