Add the chicken thighs, white beans, green chiles, onion, garlic, chicken broth, cumin, oregano, salt, and black pepper to the slow cooker. Stir once to combine.
Cover and cook on low for 6 hours or on high for 3 to 4 hours until the chicken is tender and shreds easily.
Remove the chicken to a plate, shred it with two forks, then return it to the slow cooker and stir to mix.
In a small bowl, stir together the sour cream, lime zest, and lime juice until smooth.
Ladle the chili into bowls and top each serving with a spoonful of the lime crema and a sprinkle of chopped cilantro.