Place onions in a large bowl filled with cold water and soak for about 10 minutes. Drain and dry on a clean kitchen towel.
Mix all batter ingredients together in a bowl. Place bowl over ice water.
Heat about 2 inches of oil in a heavy pan to 365 degrees F. Put dry onion rings in batter. Lift out a small handful at a time, allowing excess batter to fall back into bowl. Carefully place in hot oil and fry, turning once, three to four minutes until golden brown.
Remove and drain on a rack over a sheet pan. Salt while still hot.
Chili Lime Dipping Sauce, makes about 1/2 cup
Stir together Mayo, yogurt, chile sauce, and lime juice. Grate lime zest over the top.