Heat your pot over medium and add a splash of oil. Toss in diced onions and minced garlic, cooking until fragrant and translucent, about 2-3 minutes, with a slight caramelization around the edges.
While that cooks, season the chicken breasts with salt, pepper, and a pinch of cumin. Sear them in the same pot until golden brown, about 4-5 minutes per side. Remove the chicken, let it rest briefly, then shred it with forks.
Add chopped green chilies and ground spices to the pot, stirring for about 1 minute until fragrant and smoky.
Return the shredded chicken to the pot, pour in the chicken broth, and bring everything to a gentle simmer. Toss in drained beans and let it cook uncovered for 15-20 minutes, stirring occasionally, until the broth slightly thickens and flavors meld.
Squeeze fresh lime juice into the chili, stir well, and taste. Adjust salt, spice, or acidity as needed.
Once bubbling gently and the chicken is tender, remove from heat. Let sit for 5 minutes to allow flavors to meld.
Serve hot, garnished with chopped cilantro or a dollop of sour cream if desired. Enjoy this hearty, bright, and comforting white chicken chili with crusty bread or tortilla chips on the side.