Heat olive oil in a large pot over medium heat, then add the chopped chicken and cook until it turns opaque and starts to brown, about 5-7 minutes.
Add the minced garlic, ground cumin, and chili powder to the pot. Cook for about 1 minute until fragrant, and the garlic becomes golden and aromatic.
Pour in the chicken broth and bring the mixture to a gentle simmer, scraping up any browned bits from the bottom of the pot.
Add the rinsed white beans, chopped poblano peppers, and season with salt and pepper. Stir well, then cover the pot and let it simmer gently for about 20 minutes, until the chicken is cooked through and flavors meld.
Use a fork or tongs to shred the cooked chicken into bite-sized pieces directly in the pot, or transfer to a cutting board and chop before returning to the soup.
Squeeze the fresh lime juice into the chili and stir to brighten the flavors. Taste and adjust seasoning with additional salt, pepper, or lime as desired.
Allow the chili to simmer for another 5 minutes to incorporate the lime and develop a rich, creamy texture.
Serve the white chicken chili hot, optionally garnished with chopped fresh herbs or shredded cheese, and enjoy its silky, hearty goodness.