Grilled onions, what's the best way to grill chopped onions. This will be for a burger topping.

If you want to do chopped onions, do them in the kitchen where you have more specific control over the heat.
For BBQ, I use walla walla sweet onions (any vidilia, bermuda will work of course), slice thick and skewer with a bamboo skewer to keep the rings together, oil and slap on the grill until nice and soft with a bit of caramelization.

I use my cast iron pan on the grill for any special small item that may need grilling. I get a great smoke flavour and a perfectly sauteed/fried/grilled side.

You could cut into chunks and "kabab" them or as mentioned cut into thick slices, char, remove, then chop.

I'm not really looking for deep caramelization, but rather a nice quick char. I'm trying to limit the amount of time, and I feel that cooking them on the grill would work well. Just wasn't sure if I should but a grill basket or go with standard aluminum tins.

My method is peel the whole onion, trim the flower end but leave the stem end on. Slice in half from top to bottom. Brush the halves with oil if you like. Grill the halves flat side down, ideally over wood for some nice smokey flavor. Remove once you get nice grill marks. Then thinly slice for your burgers.

I use a grill skillet which has Perforations in it and I usually do it over a charcoal fire. Works very well especially if you're trying to grill sliced onions.

I agree with amysarah about doing them in a pan- they will truly caramelize that way and be a nice sweet balance to the grilled burger. I sauté slowly in butter with salt in a heavy pan. Once they start to brown I deglaze with some chicken broth and continue that process until they are deeply caramelized. I have also deglazed with beer and often add slivered garlic toward the end. You can do a huge pile and freeze some for later too.

I do thick slices of onion (e.g., Vidalia's) on the grill for burgers all the time, works well. If you want them chopped and caramelized, I'd do them in a skillet on the stove top. Either way, top the burger with some good blue cheese before layering on the onions and prepare to swoon.

You could cut rather thick slices of onion, brush with olive oil and grill and then chop them. You could also skewer them first to help prevent them from falling through the grates.

Never tried to grill chopped onions. Why not grill slices and then cut them up if you really want them chopped? imho, the slices are better for burger toppings, in any case.