Season chicken thighs with salt and pepper on both sides. Heat olive oil in a large nonstick skillet over medium-high heat. Cook chicken until browned, about 5 minutes per side. Add onion and garlic; cook until onion is just tender, about 5 minutes.

Stir potato, tomatoes, and chicken broth into the skillet. Cover, reduce heat, and simmer until chicken is no longer pink in the center and potato is tender, about 20 minutes. Remove from heat and stir in basil.