Preheat the grill to medium-high heat (about 400F). Season the chicken breasts with a pinch of salt, pepper, and a light drizzle of olive oil.
Grill the chicken for 6-7 minutes per side, or until the internal temperature reaches 165F. Remove from the grill, let rest for 5 minutes, then slice into bite-sized strips.
Bring a large pot of salted water to a boil. Add the 1 cup of dry orzo pasta and cook according to package directions until al dente, about 8-10 minutes. Drain well and let cool slightly.
In a small bowl, whisk together the 0.25 cup olive oil, 2 tbsp lemon juice, 1 tsp Dijon mustard, 1 tsp dried oregano, and 1 clove minced garlic to make the vinaigrette.
In a large serving bowl, combine the cooked orzo, sliced chicken, 1 cup halved cherry tomatoes, 1 cup diced cucumber, 0.5 cup chopped red onion, 0.5 cup crumbled feta, and 2 cups chopped spinach.
Pour the vinaigrette over the salad and toss gently to coat all ingredients evenly. Serve warm or chilled.