Bring a large pot of salted water to a gentle simmer. Add the chicken breasts and poach for 15–18 minutes, until they reach 165°F internally.
Remove the chicken and let it cool at room temperature for 20 minutes, then refrigerate until fully chilled, about 2 hours.
Cut the chilled chicken into 1-inch chunks.
Working in 1-pound batches, pulse the chicken in a food processor in 1-second bursts, scraping down the sides between pulses, until the pieces are small and even, about the size of rice grains.
In a large mixing bowl, whisk together the mayonnaise, grated onion with its juice, celery seed, salt, white pepper, sugar, lemon juice, and Accent seasoning if using.
Fold the ground chicken into the dressing in two additions, mixing gently until just combined.
Cover and refrigerate for at least 2 hours, or overnight for best flavor, before serving.