DIAGNOSIS: That's a worn or damaged anvil (the hexagonal shaft the bit sits in). The wobble is in the anvil itself, not the chuck, since this tool has a fixed hex drive.
FIX: The anvil is pressed into the front bearing and impact mechanism. It can be replaced, but it requires a full teardown and a press (or careful hammer and punch work) to remove the old one and install a new one. For most people, this is a service center job.
IF THAT DIDN'T WORK: Before assuming the worst, make sure it's not just a worn-out or poor-quality impact bit. Try a brand new, high-quality bit from a major brand. Cheap bits can have sloppy hex ends that exaggerate wobble.
HEADS UP: A slight wobble is somewhat normal under load, but visible wobble with no load means wear. Using it with a wobbly anvil will wear out bits faster and can lead to the anvil snapping under heavy torque.