If starting from raw chicken, season 1.5 pounds of boneless, skinless chicken breasts with salt and pepper. Poach in lightly salted simmering water for 12 to 15 minutes, or bake at 375°F for 25 to 30 minutes, until internal temperature reaches 165°F.
Let the cooked chicken rest for 10 minutes, then shred with two forks or dice into small, even pieces. If short on time, swap in 3 cups of shredded rotisserie chicken.
Add chopped almonds to a small, dry skillet over medium heat. Toast for 3 to 4 minutes, stirring often, until fragrant and lightly golden. Transfer to a plate to cool completely.
Finely dice the celery and red onion into small, uniform pieces. Rinse and pat dry the grapes, then slice them in half. Roughly chop the fresh dill, discarding tough stems.
In a small bowl, whisk together the Greek yogurt, Dijon mustard, lemon juice, salt, and pepper until smooth. Taste and adjust seasoning, adding more lemon juice if desired.
Add the shredded chicken, diced celery, diced red onion, halved grapes, toasted almonds, and chopped dill to a large mixing bowl. Pour the dressing over the top.
Use a rubber spatula to gently fold everything together until evenly coated. Avoid overmixing to keep the grapes and almonds intact.
Cover and refrigerate for at least 30 minutes before serving. Give the salad a final stir right before serving, then plate however you like best.