Season chicken with salt and pepper. Heat olive oil in a large pot over medium heat and brown the chicken on both sides. Remove and set aside.
In the same pot, add onion and cook until softened. Stir in garlic and cook until fragrant.
Add crushed tomatoes, chicken broth, and oregano. Stir well, scraping up browned bits from the pot.
Return chicken to the pot. Bring to a gentle simmer, cover partially, and cook for 35 minutes until chicken is tender.
Taste and adjust seasoning. Stir in fresh basil just before serving.
Serve hot with bread, rice, or potatoes.