An infinite ocean of constant finite depth is covered by a thin layer of ice. There is a hole in the ice (the polynya) in which there is a floating body. The motions are governed by a boundary value problem for Laplace's equation. It is solved by a hybrid method in which the water is partitioned into two regions, the unbounded region under the ice (where an eigenfunction expansion can be used) and a bounded region with a free surface (where a standard integral representation can be used). The solutions in the two regions are patched together across their common interface. A numerical scheme is developed and computational results are presented.