Heat the oil in a Dutch oven over medium-high heat and cook the chicken with 1 teaspoon salt for 6 to 8 minutes until it reaches 165°F; transfer it to a plate.
Cook the onion for 5 minutes, then stir in the cumin for 30 seconds.
Add the Hatch chiles, beans, potato, broth and remaining salt and bring to a simmer.
Cook partly covered for 20 minutes until the potato is tender, then mash the potato and about 1 cup beans against the pot.
Return the chicken for 3 minutes and finish with lime juice off the heat.