In a large saucepan of boiling, salted water, cook the orzo until al dente; drain and rinse under cool water. Return to the pot, season with salt and pepper and toss with 1 tablespoon olive oil.
Meanwhile, add 1 tablespoon balsamic vinegar to a shallow dish. Add the chicken, turning to coat, then refrigerate for 10 minutes.
In a large serving bowl, whisk together 3 tablespoons olive oil and the remaining 1 tablespoon balsamic vinegar; season with salt and pepper. Add the spinach, bell pepper and olives; do not toss.
In a medium skillet, heat the remaining 2 tablespoons olive oil over medium-high heat. Season the chicken with salt and pepper and cook until browned, about 5 minutes on each side. Let rest for 5 minutes before thinly slicing.
Add the orzo to the salad and toss. Top with the chicken, almonds and shaved Parmesan.