Squeeze juice from 1 orange (you should have 1/2 cup). Whisk orange juice, 3 Tbsp oil, vinegar, honey, salt and pepper in small bowl. Place 5 Tbsp juice mixture into a large ziptop bag. Add chicken, seal bag and marinate at room temperature 15 minutes or in refrigerator 2 hours.
Meanwhile, remove peel and white pith from remaining 3 oranges. Cut into segments; place in medium bowl.
Heat stovetop grill pan over medium heat. Remove chicken from marinade; discard bag and marinade. Grill chicken 4 to 5 minutes per side until cooked through; remove to plate and cover to keep warm.
Heat remaining Tbsp oil in a medium skillet over medium-high heat. Sauté onion 1 minute, add remaining juice mixture and cook 1 minute more. Remove skillet from heat; add orange segments.
Place spinach in large bowl; toss with half the orange mixture. Evenly divide spinach onto serving plates; place a chicken breast on top of each. Spoon remaining orange mixture on top; sprinkle with almonds.