For the chicken marinade: In a mini food processor or high-speed blender, blend the olive oil, lime juice, garlic, 1 1/2 teaspoons of the salt, 1/4 teaspoon of the black pepper, cumin, chili powder, paprika, oregano, honey, sriracha, and white vinegar until mostly smooth.
With paper towels, pat the chicken very dry on both sides. If using a whole chicken breast (which looks like a heart shape), see notes below to split it in half.
Sprinkle the chicken pieces all over (on the top and bottom of each piece) with the remaining 1 1/2 teaspoons salt and 1/4 teaspoon black pepper. With your fingers or a spoon, gently loosen the chicken skin from the flesh. Spread half of the marinade underneath the skin of the chicken pieces.
Place the chicken pieces and remaining marinade into a ziptop bag or large bowl and mix around to fully coat. Cover and marinate the chicken in the refrigerator for at least 4 hours or up to 8 hours (you can push the marinade to 12 hours, but at your own risk—the meat may start to break down somewhat because of the lime juice).
Make the Green Sauce: Add the jalapeño and cilantro to a blender (a regular blender or high speed will both work; you can also use a mini food processor, but the sauce will not be *as* smooth). Blend in long pulses until chopped.
Add the remaining sauce ingredients (garlic, yogurt, oil, lime juice, vinegar, salt, and honey) and blend for about 2 minutes, until smooth. Cover and refrigerate until ready to serve. (The sauce is excellent served right away but the flavor will intensify and the sauce will thicken a bit if it sits in the fridge overnight.)
When ready to cook the chicken, place the oven racks in the upper third and center of your oven, and preheat the oven to 425°F. Let the chicken stand at room temperature for 15 minutes prior to cooking.
Using tongs, remove the chicken from the marinade (no need to wipe it off) and place it onto a rimmed baking sheet, skin side facing up. Discard any excess marinade left in the bag/bowl.
Bake the chicken on the center rack for 15 minutes. Reduce the oven temperature to 375°F and bake for an additional 15 minutes until the chicken is cooked through. It should register 160 to 165°F on an instant-read thermometer inserted at the thickest part (the FDA directions to cook to 165°F; I prefer to remove my chicken a few degrees early, as its temperature will rise as it rests). If any pieces finish early, remove them to a plate and tent with foil while you continue baking the rest.
Turn the oven to broil. Return any chicken you pulled off early to the pan. Transfer the pan to the upper third of the oven and broil for 1 to 2 minutes, until the skin is golden and crispy. Keep a close eye on the chicken to make sure it does not burn. Don’t walk away!
Remove the pan from the oven, and allow the chicken to cool for 10 minutes. Serve with the green sauce.
Notes
Authentic Peruvian Chicken: Use the same amounts of aji panca paste in place of the chili powder and aji amarillo paste in place of the sriracha.
*Split Chicken Breast: If your split chicken breasts are HUGE compared to the thighs, you can cut them in half crosswise down through the bone into 2 smaller pieces so all of the chicken cooks in roughly the same amount of time. Place your knife firmly on top of the chicken and wiggle it slowly so you can break the bone and the knife doesn’t slip. (Note that a "split" chicken breast [how they are typically sold] is named that because it is half of an entire bone-in skin-on chicken breast—the whole breast looks like a large heart shape.)
**Jalapeños and Spiciness Level: Wear gloves or wash your hands immediately after handling jalapeños, being careful not to touch your eyes too! Adjusting the sauce spice level: For max spicy, keep the seeds of 1 jalapeño; for medium spicy, keep the seeds of 1/2 jalapeño. For the least spice (but still spicy), omit the seeds entirely. Keep in mind every jalapeño's spiciness varies. Sometimes they can be very spicy and other times barely spicy. I’d opt for less to stay on the safe side. But if you’re spicy-obsessed, add however many seeds you think you can handle.
TO STORE: Refrigerate leftover chicken and sauce separately in airtight storage containers for up to 3 days.
TO REHEAT: Rewarm chicken on a baking sheet in the oven at 350°F or in the microwave.
TO FREEZE: Freeze chicken in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating. Prepare a fresh batch of the sauce.