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Mince and mash garlic to a paste with salt. Add herbs and chop a few times together with garlic. Transfer to a small bowl and whisk in lemon juice until salt dissolves, then whisk in olive oil, paprika (if using), and 1 teaspoon pepper until combined. Set aside.
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Working with one chicken at a time, place, breast side down, on work surface. Cut out backbone with poultry shears. Turn chicken over (breast side up) and tuck wings underneath, then with the heel of your hands, press down on breast to crack breastbone so that chicken will lie flat.
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Carefully run fingers between skin and meat to loosen skin from breast, thigh, and leg. Repeat with other chicken.
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Put 1 chicken in a heavy-duty large sealable plastic bag and put bag in a large bowl. Pour half of marinade into bag and work marinade under and over skin. Seal bag, forcing out excess air, and set aside. Repeat with remaining chicken.
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Put both bags in bowl (in case of leaks) and chill at least 4 hours or overnight.
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Bring chickens to room temperature 30 minutes before roasting.
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Preheat oven to 425°F with rack in middle.
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Heat a large (12 to 14 inch) heavy skillet (not non-stick) over medium-high heat until hot, about 5 minutes.
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Remove 1 chicken from bag, discarding bag with marinade, and place, breast side down, in skillet (no need to pat it dry). Sear chicken until skin is browned, 3 to 5 minutes. Transfer, breast side up (this is most easily done with tongs and a large spatula), to a large (18- by 13-inch) rimmed sheet pan.
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Repeat with other chicken, arranging on same sheet pan.
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Roast until an instant read thermometer inserted into fleshy part of thigh (do not touch bone) registers, 170°F, 40 to 45 minutes.
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Towards last 15 minutes of roasting, arrange lemons, with a cut side down, on pan around chicken.
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Transfer chicken to a cutting board and let stand 10 minutes.
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If lemons aren’t roasted enough, return to oven while chicken rests. When browned, transfer lemons with tongs to a platter.
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Strain pan juices into a fat separator or large measuring cup and let fat rise to the top. Reserve pan juices and discard fat.
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Cut chicken into quarters and serve on platter with roasted lemons. Serve pan juices on the side.