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Heat the olive oil in a large Dutch oven or stock pot for a minute over medium heat.
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Season chicken breasts with salt, pepper, cayenne, cumin, and paprika. Add the breasts to the olive oil. Cook for about 5 minutes on each side to brown the exterior. After 10 minutes, remove the chicken, and set off to the side on a plate.
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Reduce the heat to low. Add the onion and saute for 3 minutes until translucent.
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Add in the green chilis, stock, water, hominy, and beans. Increase heat to medium. Add the chicken back into the pot. Bring the pot to a simmer. Add the quinoa.
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Simmer for 25 minutes.
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Remove chicken and shred using two forks. Add the chicken back to the pot.
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Turn the heat off. Add lime juice, salt and pepper to taste, and fresh chopped cilantro.
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Serve hot with chips and sour cream and hot sauce!