Pat the chicken dry with paper towels and season it lightly with a pinch of salt and pepper on both sides.
Heat the olive oil in a large pot or Dutch oven over medium heat until shimmering.
Add the chicken breasts to the pot and sear until lightly golden on each side, about 3 to 4 minutes per side, without cooking them through completely.
Transfer the partially cooked chicken to a plate and set it aside while you build the flavor base.
Add the diced onion and minced jalapeño to the same pot and sauté over medium heat until the onion is softened and translucent, about 4 to 5 minutes, stirring occasionally.
Stir in the minced garlic and cook until fragrant, about 30 seconds, making sure it does not brown.
Add the diced green chiles, cumin, chili powder, smoked paprika, dried oregano, salt, and black pepper to the pot and stir to coat the vegetables in the spices.
Pour in the chicken broth, scraping up any browned bits from the bottom of the pot to incorporate that flavor into the chili.
Return the seared chicken and any accumulated juices to the pot, nestling the pieces into the liquid.
Bring the mixture to a gentle simmer over medium heat, then reduce the heat to medium low, cover, and cook until the chicken is cooked through and very tender, about 15 to 18 minutes.
Transfer the cooked chicken to a cutting board and let it rest for a few minutes until cool enough to handle comfortably.
Shred the chicken using two forks or tongs into bite sized pieces, discarding any large fatty bits if desired.
While the chicken rests, reduce the heat under the pot to low and add the cubed cream cheese to the hot broth, whisking or stirring frequently until it is fully melted and smooth.
Slowly pour in the heavy cream while stirring continuously, keeping the heat low so the dairy warms gently without boiling or separating.
Return the shredded chicken to the pot and stir well to distribute it evenly through the creamy broth.
Simmer the chili uncovered over low heat for 8 to 10 minutes, stirring occasionally, until it has thickened to a rich, creamy consistency that coats the back of a spoon.
Stir in the fresh lime juice and taste the chili, adjusting with additional salt, pepper, or jalapeño if you prefer more heat.
If the chili is thicker than you like, stir in a splash of additional chicken broth to loosen it to your preferred texture.
If the chili is thinner than you like, continue to simmer it uncovered over low heat for a few more minutes, stirring often, until it reduces and thickens further.
Ladle the spicy keto white chicken chili into bowls and top with shredded cheese, sour cream, cilantro, avocado, and jalapeño slices as desired before serving.
For meal prep, let the chili cool completely, then portion it into airtight containers and refrigerate for up to 4 days or freeze for up to 2 months.
Reheat the chili gently on the stove over low to medium low heat or in the microwave on medium power, adding a splash of broth or cream if it has thickened in the fridge.