The technique of intensity interferometry is proposed as a probe of the spatial configuration of two-neutron haloes. After exploring the sensitivity of interferometry to the n-n configuration, it is demonstrated that the application of the standard method for constructing the correlation function is not valid for halo neutrons. A new iterative method is presented and applied to measurements of the dissociation of 6 He, 1 1 Li and 1 4 Be. The correlation functions for these systems have thus been extracted for the first time and the corresponding root-mean-square n-n separations estimated. The results are in agreement with the predictions of available three-body models.