Magnetic domains in a garnet thin film under alternating magnetic fields up to 2000 Hz have been investigated at room temperature. Domain structures and motions have been observed. When the field frequency is low, the magnetization changes periodically, and the domain pattern has a labyrinth structure. When the amplitude and the driving frequency of the field are increased, irregular oscillations of the magnetization appear, and chaotic motions of the domain are observed. In this region, domain structures have a disk-like shape. These disks grow from some crystal defects, and a growing point shows a branch-like form.