Whisk together peanut oil and mustard in a large bowl. Whisk in beer and lemon juice until mixture is smooth. Stir in garlic, salt, pepper, basil and thyme. Add chicken pieces and turn to coat well. Cover and refrigerate 2 to 12 hours.
In a charcoal grill, heat about 5 dozen charcoal briquettes until covered with white ash. Meanwhile, drain chicken and discard marinade.
Use large tongs to push hot briquettes to one side of the grill. Away from the grill, spray grill rack evenly with non-stick cooking spray; place on grill. Place chicken parts on grill rack, on the coals side. Cook uncovered until skin is crisp, about 10 minutes, moving and turning as needed with clean tongs to prevent charring.
Move chicken parts to the cool side of the grill; cover and cook until meat is opaque throughout and juices run clear, about 10 to 15 minutes more.
Serve with mustard and German sauerkraut, such as the Hengstenberg, Gundelsheim or Kühne brands.