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Preheat oven to 350 degrees. Cover a sheet pan with parchment paper.
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Lay the chicken breast-side-down on a cutting board. Using a sharp chef's knife or kitchen shears, cut the chicken in half along the back bone, staying as close to the bone as possible. Turn the chicken over and cut the chicken through the center of the breast bone. Separate the two halves and lay them skin-side-up on the sheet pan.
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Squeeze the juice of 1 lemon onto the chicken, and rub it on the front and back of the chicken halves. Pour a little less than half of the olive oil over the chicken and rub again to evenly coat the skin. Generously season the chicken with salt and pepper. Sprinkle 1 tablespoon of the oregano and half the garlic over the chicken.
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Put the potatoes in a large bowl. Add the remaining olive oil, remaining garlic, remaining oregano, and the juice of the second lemon. Season generously with salt and pepper and toss to coat the potatoes.
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Arrange the potatoes on the sheet pan around the chicken. Drizzle any liquid remaining in the bowl on top.
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Roast the chicken and potatoes until both are golden and crispy and the chicken is cooked through, about 1 hour and 15 minutes.
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Carve the chicken and arrange along with the potatoes on a serving platter. Pour any extra drippings from the pan over the chicken (be sure to scrape up all the browned bits from the pan along with the sauce -- those are the very best parts). Cut the remaining lemon into wedges and arrange alongside the chicken.