Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced red onion and jalapeño. Sauté for 5 minutes until softened.
Add the minced garlic, cumin, and oregano. Stir constantly for 1 minute until fragrant.
Pour in the chicken broth, salsa verde, and canned green chiles. Stir to combine.
Add the raw chicken breasts and the drained white beans to the pot. Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 20-25 minutes until the chicken is cooked through and tender.
Remove the chicken to a cutting board and shred with two forks. Return the shredded chicken to the pot.
Stir in the fresh lime juice and half of the cilantro. Taste and season with salt and pepper if needed.
Ladle into bowls and top generously with sliced avocado, remaining cilantro, and extra red onion if desired.