Heat oil in a large heavy pot over medium heat. Add onion; cook, stirring occasionally, until softened, about 5 minutes. Add garlic; cook, stirring constantly, until fragrant, about 1 minute. Add beans, chicken, potatoes, broth, thyme, salt and pepper. Bring to a boil over medium-high heat; reduce heat to maintain a simmer. Simmer, covered, until the potatoes are tender and an instant-read thermometer inserted in the thickest portion of the chicken registers 165 degrees F, about 18 minutes.