Lay onions and steak in a 9- by 13-in. baking dish. Mix remaining ingredients in a small bowl and pour over onions and steak, turning ingredients to coat. Chill at least 1 hour and up to overnight.
Heat grill to high (450° to 550°). Grill steak, covered, turning once and moving it from flame as needed to prevent charring, until done the way you like, about 8 minutes for medium-rare. In the last few minutes, add onions to grill, laying them perpendicular to the grates. Cook, turning as needed, until onions start to soften and grill marks appear.
*Buy at Latino markets, farmers' markets, and some grocery stores.