Combine lime juice, soy sauce, vinegar, salt, garlic, sugar, cumin, chili powder, smoked paprika, and oregano in a blender. Blend until smooth.
Pour marinade over chicken in a baking dish or large zip-lock bag. Using your finger, loosen the skin from the chicken pieces and spoon additional marinade under the skin. Marinate chicken for at least 6 hours, and up to 24 hours.
Preheat oven to 425 degrees. Roast on middle rack on foil or parchment-lined baking sheet for 45 minutes.
Meanwhile, slice potatoes lengthwise.
Toss potatoes in large bowl with oil, salt, and pepper.
Line rimmed baking sheet with parchment paper. Roast for 25 minutes on bottom 3rd of the oven, stirring potatoes once during roasting process.
Serve chicken and potatoes accompanied by Peruvian green sauce.