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(1). 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).