Preheat the oven to 400°F (200°C). Line a baking sheet with aluminum foil and lightly spray the foil with non-stick cooking spray.
Pat the 4 boneless skinless chicken breasts dry with paper towels. If any breasts are unevenly thick, place them between two sheets of plastic wrap and gently pound to an even thickness.
In a small bowl, mix 1/4 cup mayonnaise and 1 tablespoon lemon juice until smooth.
In a separate shallow bowl, combine 30 crushed Ritz crackers (about 1 cup), 1/4 cup grated Parmesan cheese, and 2 teaspoons dried basil. Stir until evenly mixed; the crackers should be fine crumbs.
Coat each chicken breast with the mayonnaise mixture, allowing excess to drip off, then press both sides of each breast into the cracker mixture so the crumbs adhere.
Arrange the coated chicken breasts on the prepared baking sheet, spaced apart so they bake evenly.
Bake for about 20 minutes, or until the chicken is cooked through (no longer pink in the center and registers 165°F on an instant-read thermometer). Let the chicken rest a few minutes before serving.