Heat olive oil in a medium pot over medium-high heat. Season chicken with salt and pepper. Add chicken to pot and cook, stirring occasionally until golden, but not cooked through (2 to 3 minutes).
Add ½ cup salsa verde and scrape up any bits from the bottom of the pot. Cook 1 minute.
Add broth. Bring to a boil. Reduce heat to medium-low and simmer for 5 minutes.
Increase heat to medium. Add beans and cook another 5 minutes.
Stir in remaining salsa verde, salt and pepper. Remove from heat and let stand for 10 minutes. Stir before serving. Top with green onions and lime, desired.