This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward modelling used for correlation and multiple fitting of the measured diffraction spots relative to individual grains. This enables not only to identify individual grains, but also their position and orientation in the sample. The feasibility and performance of the Laue3DND approach are tested using multi-grain synthetic datasets from cubic (α-Fe) and tetragonal (YBaCuFeO5) symmetries. Next, experimental results from two data sets measured at the FALCON instrument of Helmholtz-Zentrum Berlin are presented: A cylindrical alpha iron (α-Fe) reference sample with 5 mm diameter and 5 mm height, as well as a 2 mm3 layered perovskite (YBaCuFeO5). Using Laue3DND, we were able to retrieve the position and orientation of 97 out of 100 grains from a synthetic α-Fe data set, as well as 24 and 9 grains respectively from the α-Fe and YBaCuFeO5 sample measured at FALCON. Results from the synthetic tests also indicate that Laue3DND is capable of indexing 10 out of 10 grains for both symmetries in two extreme scenarios: using only 6 Laue projections and using 360 projections with extremely noisy data. The precision achieved in terms of spatial and orientation resolution for the current version of the method is 430 μm and 1° respectively. Based on these results obtained, we are confident to present a tool that expands the capabilities of standard Laue diffraction, providing the number, position, orientation and relative size of grains in oligocrystalline samples.