A round onion tends to move on a cutting board, which can be dangerous, so use one hand to hold it firmly in place. Use the other hand to cut straight down. You want thick, even slices.
Step 2:
Slices thinner than [conversion imperial="⅓ inch" metric="8 millimeters"] often fall apart on the grill, and slices that are not the same thickness from edge to edge cook unevenly and fall apart.