  Fully localised solitary waves are travelling-wave solutions of the
three-dimensional gravity-capillary water wave problem which decay to zero in
every horizontal spatial direction. Their existence for water of finite depth
has recently been established, and in this article we present an existence
theory for water of infinite depth. The governing equations are reduced to a
perturbation of the two-dimensional nonlinear Schr\"{o}dinger equation, which
admits a family of localised solutions. Two of these solutions are symmetric in
both horizontal directions and an application of a suitable version of the
implicit-function theorem shows that they persist under perturbations.
