1. In a large baking dish, whisk together lemon juice, 1/4 cup olive oil, shallot, and 1/4 teaspoon black pepper. Add chicken to the baking dish, tossing to coat.
2. Cover and marinate in the refrigerator for at least 30 minutes or up to four hours.
3. Heat your grill or grill pan over high heat. Remove chicken from marinade and season with salt on both sides. Grill for two to three minutes per side or until golden brown and just cooked through.
4. Heat a skillet over low heat. Add pastrami strips and cook for about 20 minutes, stirring every five minutes. Season with remaining pepper.
5. Spoon over grilled chicken.