1. Toast the walnuts in a small skillet over medium-high heat, stirring them frequently, about 2–3 minutes. Transfer the toasted walnuts to a bowl and set aside.
2. Cut both ends off of each orange. Stand the fruit on a cutting board. With a sharp knife, cut the skin and white pith off of both oranges, starting from top and working toward the bottom. Holding the orange in your hand over a bowl, cut the sections from the orange between the membranes, letting the sections fall into the bowl. Squeeze the membrane to extract all of the juice; reserve orange juice. Remove the sections to a medium bowl.
3. Place the cucumbers in a small bowl and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper.
4. Transfer 1 tablespoon of the orange juice to a small bowl. Add the vinegar, olive oil and 1/4 teaspoon each salt and pepper. Whisk well to combine. Transfer the mixture to a small pitcher for serving. Set aside.
5. Lightly spray the chicken breasts with olive oil spray and sprinkle with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Preheat a grill pan on high heat for 1 minute. Grill the chicken until cooked through, about 5 minutes per side. Transfer the chicken breasts to a cutting board, let them stand 5 minutes, then cut each into slices on the diagonal.
6. Divide the romaine lettuce leaves among 4 plates; top each with equal amounts of the cucumber slices and orange segments. Add 4 ounces chicken, and 1 1/2 teaspoons walnuts to each plate. Sprinkle each with chives and serve immediately, with the dressing served on the side.