While not ideal, it is possible. Heck, my smoker only has one burner, and it isn't an offset model.
The trick, I think, will be to get a foil pan of some sort (I get the cheap ones from a local hardware store) and put the wood chips in that. Next, set the grill on low and see what the lowest temp you can hold it at is. Once the pan gets hot enough, the chips (even if they were soaked in water) should smolder and smoke. Hopefully the grill will settle in somewhere around the 225F range. If it's lower, go up in temp. If it's higher, just do the best you can (maybe prop the grill lid open a bit).
If you can give them the time, pork butts are very forgiving as far as smoking/BBQing.
Another option - If the grill simply isn't going to work for a low/slow cooking, add your chips to the grill and get it good and smokey in there. Add the pork butt, and leave it in the smoke for 30 min to an hour, then transfer to an oven and cook it like Gretchen noted. It won't be perfect, but it should still have some smoke to it when it's done.