Season chicken with salt and pepper. On a large plate, dredge chicken in flour.
Heat 2 tablespoons of olive oil in a large skillet on medium-high heat.
Add chicken and brown for about 4 minutes until it turns nice golden color. Flip the chicken over to the other side and brown the other side for about 4 minutes on medium heat.
Remove the chicken to the plate.
Add artichokes, sun-dried tomatoes, capers, and lemon juice to the same skillet. Stir to combine, on medium heat. Reduce heat to medium-low. Add 2 or 3 tablespoons olive oil, stir in to combine.
Push the vegetables to the sides of the skillet, and add the chicken back.
Cook the chicken and the vegetables on low-medium heat for about 5-10 more minutes, covered, until the chicken is completely cooked through and no longer pink in the center.
Depending on your stove, you might have to cook either on medium or on medium-low heat to cook the chicken through.
Serve immediately. Make sure to spoon the olive oil mixture of vegetables from the skillet over the chicken.