Mix yogurt, 1 tablespoon lime juice, cumin, chipotle, and 1/2 teaspoon salt. Coat chicken; refrigerate 30 minutes, included in prep time.
Heat 12-inch skillet over medium. Warm tortillas individually about 20 seconds per side; stack under clean towel.
Wipe empty skillet with paper towel; add 1 tablespoon oil and raise to medium-high. Scrape excess marinade from chicken; cook in 2 batches 3 to 4 minutes per side to 165°F each. Discard raw marinade.
Rest cooked chicken on clean board. Add remaining oil, poblano, red pepper, onion, and remaining salt; cook 7 to 9 minutes until tender with browned edges.
Thinly slice chicken across grain. Return with juices and remaining lime juice; toss with peppers over low 1 minute.
Divide among 8 warm tortillas; serve 2 fajitas per portion.