Combine all the ingredients for the vegetable marinade in a bowl and stir well. Pour over vegetables and toss well. Refrigerate for at least an hour before cooking.
Season the chicken on both sides with salt and rosemary. Heat one tablespoon of olive oil in a large skillet set over medium high heat and add the chicken. Cook for about 7 minutes and turn over. Squeeze over lemon juice and cook other side for about 7 minutes or until chicken is cooked through. Remove chicken from pan and set aside.
In the same skillet, add the vegetables with all the marinade. Cook, stirring occasionally for about 15 minutes. Remove from heat.
Place the chicken fillets on a cutting board and cut them into thin slices. Arrange the arugula leaves on a large serving dish, top with vegetables and chicken. Serve immediately.
*A note on times provided: appliances vary, any prep and/or cook times provided are estimates only.