In a small bowl, whisk together lime juice, 1/4 cup oil, honey, cumin, and red pepper flakes. Season with salt and pepper.
In a large resealable plastic bag, combine chicken and half the dressing. Let marinate at least 30 minutes and up to 6 hours.
When ready to cook, heat 2 tablespoons oil in a grill pan over medium-high heat. Add chicken and grill until charred and fully cooked through, 8 minutes per side. Let rest 10 minutes, then slice into strips.
Add peppers and onions to pan over medium-high heat and grill until charred and soft, 10 minutes.
In a large bowl, combine romaine, chicken, peppers and onion, and avocado. Toss with remaining dressing.
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