How to Make It
In a medium bowl, combine 2 tablespoons of the lime juice with the garlic, chipotle and sugar; season with salt and pepper. Add the chicken and marinate for 20 minutes.
In a large skillet, heat 1 tablespoon of the oil until just smoking. Add the red, yellow and green bell peppers and the poblano chile and sauté over moderately high heat, stirring occasionally, until slightly softened and beginning to brown, about 4 minutes. Add the onion and cook until tender and all the vegetables are slightly charred, about 4 minutes. Transfer to a large plate.
Heat the remaining 1 tablespoon oil in the skillet. Add the chicken and cook over moderately high heat until brown on the bottom, about 4 minutes. Turn the chicken, reduce the heat to moderate and cook the other side until brown, another 4 minutes. Transfer the chicken to a cutting board and slice 1/2 inch thick.
Meanwhile, add the chicken stock to the skillet and simmer over moderately high heat, scraping the pan to loosen any browned bits, until slightly reduced. Strain the sauce through a fine-mesh sieve. Wipe out the skillet and return the sauce. Add the butter and remaining 1 teaspoon lime juice and swirl over moderately high heat until incorporated. Return the peppers, chicken and any juices to the sauce and heat through gently. Serve warm.