Pat the chicken dry and season lightly with 1/2 teaspoon salt and a few grinds of black pepper. Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat and brown the chicken for 3 minutes per side until golden—this builds extra flavor. Transfer the chicken to a plate and set aside.
Reduce heat to medium. Add the diced onion and chopped jalapeño to the same pot and sauté 4 to 5 minutes until softened. Stir in the minced garlic and cook 30 seconds until fragrant.
Stir in the cumin, oregano and lime zest, toasting the spices for about 30 seconds. Pour in the chicken broth, scrape up any browned bits from the bottom of the pan, then add the drained green chiles and the rinsed white beans.
Return the browned chicken to the pot. Bring to a gentle simmer, then reduce heat to maintain a low simmer and cover. Cook 18 to 22 minutes, or until the chicken is cooked through (internal temperature 165°F).
Remove the chicken to a cutting board and shred with two forks. Meanwhile, take about 1 1/2 cups of the bean mixture from the pot and pulse in a blender or mash with a potato masher until mostly smooth, then stir the puréed beans back into the soup — this lightly thickens the chili without cream.
Return shredded chicken to the pot, stir in the Greek yogurt and lime juice, and simmer uncovered 3 to 5 minutes to warm through and meld flavors. Taste and adjust seasoning with additional salt or lime if needed.
Turn off the heat and let the chili rest 8 to 10 minutes — this helps flavors develop and thickens slightly. Ladle into bowls and finish with chopped cilantro, avocado slices and a dollop of yogurt if desired.