Line two baking sheets with parchment paper. Preheat oven to 400°F.
In a large bowl, whisk together the first five ingredients.
Place ONLY 3/4 cup of the crushed crackers in a gallon-sized zip-top plastic bag.
Add HALF of the chicken cubes to the mayonnaise mixture and toss gently. Using a slotted spoon, transfer the chicken to the zip-top bag and shake to coat all pieces of chicken. Remove the chicken and place on a prepared baking sheet. Repeat with the remaining chicken and crushed crackers.
Bake at for 8-10 minutes on each side or until chicken is no longer pink and crackers are beginning to turn golden.