A novel mechanism for ramified island growth in the initial stages of metal heteroepitaxy is reported. Scanning tunneling microscopy measurements reveal that copper islands on Ni(100), as they grow in size, undergo a shape transition. Below a critical size of approximate to 480 atoms, compact islands form, while above this size they develop a ramified shape. This effect is not of kinetic origin and has been observed in an extended range of growth temperature (250-370 K) and deposition Aux (10(-5)-10(-2) monolayer/s). The shape transition is ascribed to the island size dependent strain relaxation.