Whisk the sour cream, oregano, lemon juice, salt, pepper, minced garlic, and oil in a large bowl or resealable bag until the mixture looks smooth and evenly seasoned. The marinade should have no dry pockets of oregano or streaks of oil sitting apart from the sour cream.

Add the chicken thighs and turn them until every surface is coated, then cover and refrigerate for 24 hours, or for at least 3 hours. The chicken should sit fully covered in the thick, herb-speckled marinade.

Heat the oven to 425°F, line the lower portion of a broiler pan with foil, and lightly oil the upper rack. The rack should sit above the lined pan so drippings can collect below the chicken.

Arrange the thighs skin-side up on the prepared rack and roast for 45 minutes, until the internal temperature reaches 165°F. Insert the thermometer into the thickest part of a thigh without touching bone, and look for deeply golden skin with rendered fat beneath it.

Serve the chicken while hot after removing it from the roasting pan. The skin should be crisp at the edges and the juices should settle back into the meat before carving.