Heat the oil in a Dutch oven over medium-high heat and brown the chicken with 1 teaspoon salt for 6 to 8 minutes until it reaches 165°F; transfer it to a plate.
Cook the onion in the same pot for 5 minutes, then stir in the garlic, cumin and oregano for 30 seconds.
Mash 1 can of beans with 1/2 cup broth until coarse and add it to the pot with the whole beans, green chiles, remaining broth and salt.
Simmer uncovered for 18 minutes, stirring occasionally, until the broth lightly coats a spoon.
Return the chicken for 3 minutes, remove the pot from the heat and stir in the lime juice.