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Heat one tablespoon of olive oil in a medium saucepan or Dutch oven over medium heat.
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Add half of the diced onion and sauté for 4-5 minutes.
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Stir in the cumin and chili powder.
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Season the chicken with salt and pepper.
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Add the chicken, salsa, and chicken stock to the pan and bring to a boil.
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Reduce the heat to simmer and cook, covered, for 15-20 minutes, or until the chicken is completely cooked through.
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Meanwhile, melt the remaining olive oil in a separate pan over medium heat.
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Add the other half of the onion and all of the bell pepper and sauté for 5-6 minutes, or until slightly softened. Set aside.
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Remove the chicken from the pan and set aside to cool.
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Bring the stock in the pan back to a boil and reduce for 5-8 minutes.
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Once the chicken has cooled enough to handle, shred with two forks.
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Place back into the pan and reduce the heat to low.
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Stir in the lime juice and adjust the seasonings to taste.
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Serve on leaves of lettuce, topped with sautéed onions and peppers.