Let P be a Poisson process of intensity 1 in a square Sn of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that, for c‹ccrit, Gn,⌊clogn⌋ is disconnected with probability tending to 1 as n →∞ and, for c‹ccrit, Gn,⌊clogn⌋ is connected with probability tending to 1 as n →∞. This answers a question posed in Balister et al. (2005).