Place a 17-inch paella pan on the grill, cover, and heat until hot, about 2 minutes.
Add 1 to 2 tablespoons of olive oil and the chorizo to the pan, close the grill, and cook, stirring occasionally, until the sausage is starting to brown and the fat is rendered, about 2 to 3 minutes. Using tongs or a slotted spoon, transfer the chorizo to a large bowl; set aside.
There should be a thin layer of rendered fat in the pan. If there’s not enough, add another tablespoon of olive oil.
Add the seasoned chicken to the pan in a single layer, close the grill, and sear, stirring occasionally, until both sides of the chicken pieces are golden brown, about 6 minutes total. (You will need to rotate the pan occasionally on the grill to evenly distribute the heat.) Using tongs or a slotted spoon, transfer the chicken to the bowl with the chorizo; set aside.