Cut chicken breasts crosswise into 1/2-in.-thick slices, then cut each slice in half lengthwise so you end up with finger-size pieces. Combine chicken, soy sauce, cornstarch, and 1/4 tsp. white pepper in a small bowl and toss to coat evenly. Set aside.
Zest orange into a small bowl. Segment orange: With a sharp knife, trim off ends and set a cut side down on a cutting board. Following the curve of the fruit, trim off peel and white pith. Set a strainer in a separate bowl and, working over bowl, slice segments free of membranes. Squeeze juice from membranes into strainer. Measure 3 tbsp. juice and add to bowl with zest. Set orange segments aside.
Cut lemon in half and set one half aside. Zest and juice the other half into bowl with orange juice and zest, then add brown sugar, sesame oil, and remaining 1/4 tsp. white pepper. Set sauce aside.
Heat vegetable oil in a large nonstick pan over medium-high heat. Add onion and ginger and cook until just beginning to brown, about 2 minutes. Push onion and ginger to one side of pan and add chicken in a single layer. Let sear undisturbed 2 minutes. Add celery and citrus sauce and cook, stirring constantly, until sauce thickens and chicken is cooked through, about 2 minutes more.
Remove from heat and stir in reserved orange segments. Pour into serving bowl or onto a platter. Squeeze juice from reserved lemon half over chicken and shower with slivered green onion. Serve with steamed rice if you like.