Start by cubing your chicken into even, bite-sized pieces so everything cooks at the same rate. Dice the onion finely and mince your garlic while the pan heats up on the stove. If you're using fresh Hatch chiles instead of frozen roasted ones, char and peel them first. Having everything prepped before the pan gets hot makes this whole green chili chicken stove top method move quickly and smoothly.
Heat the olive oil in your skillet over medium-high heat until it shimmers. Season the chicken generously with salt, pepper, cumin, and smoked paprika, then add it to the pan in a single layer. Let it sear undisturbed for a few minutes so it browns properly instead of steaming. Once golden on both sides, remove the chicken and set it aside on a plate.
In the same skillet, add the diced onion and cook until it turns soft and translucent, scraping up any browned bits left behind. Stir in the garlic and cook for about thirty seconds, just until fragrant. Add the chopped Hatch chiles next and let them warm through, releasing their smoky aroma into the pan. This base is really the heart of the whole dish.
Lower the heat slightly and add the softened cream cheese directly into the skillet. Stir continuously until it starts to melt into the onions and chiles. Slowly pour in the chicken broth while stirring, which helps the cream cheese loosen into a smooth, pourable sauce. Keep stirring until there are no lumps left and the sauce looks silky.
Add the seared chicken back into the skillet along with any juices that collected on the plate. Stir everything together so the chicken is fully coated in that creamy green chile sauce. Reduce the heat to low and let it simmer gently, which allows the flavors to meld and the chicken to finish cooking through.
Sprinkle the shredded Monterey Jack cheese over the top and stir it in until fully melted and glossy. If you'd rather do the green chili chicken bake version, transfer everything to a greased baking dish at this point and top with extra cheese. Bake at 375°F for about fifteen minutes until bubbly around the edges.
Once the chicken reaches a safe internal temperature, pull the pan off the heat and let it rest for a couple of minutes. Top with freshly chopped cilantro and a good squeeze of lime juice right before serving. This last step brightens the whole dish and keeps it from tasting flat.