Make the chicken: Pat both sides of your chicken dry with a paper towel. Season with oregano, salt and pepper, and set aside to prep the skillet.
Drizzle your olive oil into the bottom of a large skillet. Heat the skillet over medium heat until warmed. Gently lower the chicken breasts into the hot pan. Cook for 5 to 7 minutes on the first side, or until lightly browned.
Flip the chicken breasts, then cook for an additional 5 to 7 minutes on the other side or until the chicken is cooked through. The chicken should register an internal temperature of at least 165°F and the juices should run clear. Set aside the chicken to rest and cool for 10 to 15 minutes before cutting.
Make the vinaigrette: In a small bowl, whisk together lemon juice, vinegar, olive oil, and salt. Set aside.
Make the salad: In a large bowl, combine the chopped lettuce, red onion, tomatoes, and croutons. Slice your cooled chicken into 1 inch strips and add to the bowl as well.
Pour the vinaigrette over your salad and toss to coat everything in the dressing. Taste for seasoning and adjust if needed. Serve right away to prevent having the croutons soften.