Prepare the chicken by shredding or dicing it into bite-sized pieces. If starting from scratch, boil or roast the chicken until fully cooked, then chop it up.
In a separate bowl, combine mayonnaise, Greek yogurt, Dijon mustard, fresh lemon juice, salt, and pepper. Whisk until smooth and creamy.
In a large mixing bowl, combine the prepared chicken, halved grapes, and diced celery. Pour the dressing over the mixture and stir gently until well coated.
Cover the bowl with plastic wrap and refrigerate for at least 30 minutes to allow flavors to meld.