Heat 1 tablespoon of the oil in the largest skillet you have (at least 12 inches) over medium-high heat until shimmering. Add the onions and season with 1/4 teaspoon of the salt.
Cook, tossing often with tongs to prevent burning, until they begin to soften and brown, about 3 minutes.
Cook the peppers, jalapeño, and garlic until fragrant.
Add the bell peppers, jalapeño, and garlic and season with 1/4 teaspoon of the salt.
Cook, again tossing often, until starting to brown and the garlic is quite fragrant, about 3 minutes. Brown the chicken with the spices.
Transfer the vegetables to a plate.
Return the pan to medium-high heat (no need to clean) and add the remaining 1 tablespoon oil. Add the chicken and season with the remaining 1/2 teaspoon salt, oregano, and cumin.
Cook undisturbed until the chicken has some golden-brown color, flipping halfway through, about 6 minutes total.
Add the vegetables back to the pan, add the lime juice, and finish cooking. Cook until the chicken is cooked through and the peppers are soft, about 2 minutes moreServe the chicken and vegetables in warmed tortillas with sour cream and extra lime wedges for squeezing.
Storage: Leftovers can be refrigerated in an airtight container for up to 4 days.