Remove the Backbone – Use paper towels to dry the surface of the chicken. Place the chicken on a cutting board, breast-side down. Using sharp kitchen shears or poultry shears, remove the backbone, cutting along the spine from the neck down to the tail. Discard the backbone.
Flatten the Chicken - Place the chicken breast-side up. Rotate the legs outward so they splay to the sides. Place both hands on top of the breastbone and press down firmly until you hear a crack, this helps the chicken lay flat. Transfer the chicken to a wire rack set over a baking sheet lined with foil, positioning it so the breasts are centered and the legs are near the edges for more even cooking.
Marinate the Chicken - In a medium bowl, whisk together the lime juice, olive oil, vinegar, ají amarillo pepper paste (if using), paprika, cumin, garlic, salt, black pepper, and oregano. Rub 1 tablespoon of marinade under the skin of each breast. Brush the remaining marinade on the surface of the entire chicken. Cover and refrigerate for at least 30 minutes, or up to 24 hours.
Roast the Chicken - Set oven rack to middle position and heat to 400°F (204ºC). Cook until the thickest part of the breast reaches 160 to 165°F (71 to 74°C) and thighs reaches 165 to 170°F (74 to 77°C), about 1 hour. Tent the chicken with foil if the surface browns too fast. Rest for at least 10 minutes before carving and serving.
Make the Sauce - In a blender or food processor, add the jalapenos, garlic, cilantro, mayonnaise, sour cream, ají amarillo pepper paste (if using), lime juice, vinegar, salt, and pepper, over high speed until smooth. With the blender running on low speed, slowly drizzle in the olive oil. Season with salt and pepper to taste.
To Serve - Cut the chicken into pieces and serve with the green sauce.
Notes
Green Sauce Yield: About 1 1/4 cups
Ají Amarillo Substitute: Swap the yellow pepper paste for roasted and pureed jalapeños, serranos, habaneros, sweet yellow peppers, or manzano. Add ají panca, sriracha, canned chipotle, or canned fire-roasted green chilies.
Make the Sauce Spicier: Keep the seeds and membrane in the jalapeno or add more aji amarillo paste.
Storing: Refrigerate the chicken and sauce in an airtight container for up to 5 days.