Heat 2 tablespoons olive oil in a skillet over medium-low heat. Place onions to the skillet; cook and stir until the onions are soft, 5 to 7 minutes. Add mushrooms and garlic; cook and stir until mushrooms are soft, 7 to 10 minutes. Pour the mushroom mixture into a bowl.
Heat 1 tablespoon olive oil in the skillet over medium-high heat. Place chicken in the skillet; cook until the chicken is golden brown and no longer pink in the center, 7 to 10 minutes per side. Stir the mushroom mixture in with the chicken and season with salt and pepper. Add tomatoes; cook and stir until tomato juice begins to simmer, 5 to 7 minutes. Stir in table cream; simmer until flavors are combined, 1 to 3 minutes.