For the Tex-Mex chili rub: Mix together the paprika, brown sugar, chili powder, cumin, chipotle chile powder, garlic powder and 1 teaspoon salt in a small bowl. Toss the chicken in a container with the olive oil and lime juice, then rub with the spice mixture. Refrigerate, covered, for at least 30 minutes and up to 2 hours before cooking.
For the peppers and onions: Heat a cast-iron pan over medium-high heat until hot. Toss the peppers and onions in a bowl with the olive oil, lime juice and 1 teaspoon salt. Add the pepper-onion mixture to the hot pan and cook, stirring occasionally, until the vegetables are tender and the edges are charred, 8 to 10 minutes. Set aside.
Prepare a grill for medium-high heat and brush the grill grates with oil.
Grill the chicken breasts until marked and cooked through, 5 to 6 minutes per side. Transfer to a cutting board and thinly slice.
Serve with the warm tortillas and toppings.
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