Heat oil in a 10-inch skillet over high heat. Season chicken generously with salt and pepper; add chicken to skillet, skin side-down and place a 10-inch heavy-bottomed skillet on top of chicken. Place two heavy soup cans or a brick in second skillet to weigh down.
Reduce heat to medium and cook chicken until skin is golden brown and crisp, about 18 minutes. Remove top skillet and weights and turn chicken; pour off excess fat from skillet.
Squeeze lemon juice over chicken and add stock. Cook until an instant-read thermometer inserted into the chicken thigh registers 160 degrees, about 3 minutes.
Season tomatoes with salt and pepper and divide evenly between two plates. Place each chicken half on a plate and serve immediately with pan juices.