Put the chicken in a large resealable plastic bag.
Whisk the ketchup, brown sugar, orange zest and juice, lemon zest and juice, garlic, Dijon, Worcestershire sauce, cumin, smoked paprika, 1 teaspoon salt, and a few grinds of black pepper together in a 4-cup liquid measuring cup (or alternatively a medium bowl) until combined.
Remove 1 cup of the sauce and add the remaining sauce to the resealable plastic bag with the chicken. Seal and toss the bag to evenly coat the chicken. Marinate the chicken in the refrigerator for 1 hour and up to overnight.
Meanwhile, add the remaining sauce to a small saucepan. Bring the sauce to a boil over medium-high heat. Reduce the heat to low and simmer until the sauce thickens, about 10 minutes. Reserve reduced sauce for glazing and serving.
Prepare a grill for medium-high heat.
Remove the chicken from the marinade and allow any excess marinade to drip off. Arrange the chicken skin-side down on the grill, leaving some space between each. Cook until deep grill marks form and releases easily from the grill, about 4 minutes. Flip the chicken skin-side up. Cover the grill and cook until an instant-read thermometer inserted into the thickest part of each thigh reads 165 degrees F, 20 to 25 minutes more.
Brush the skin side of the chicken with some of the reduced sauce. Flip the chicken pieces and brush the other side of the chicken with the sauce and continue to cook, sauce-side down, for an additional minute. Flip and grill for 1 minute more. Transfer the chicken to a platter and let rest for 5 minutes.
Serve the chicken with the remainder of the sauce.
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