Marinate your chicken—ideally the night before, but honestly, just as long as you can before cooking it. Place the chicken thighs in a bowl or large Ziplock bag with the salt, the juice of one lemon, and the dried oregano. Massage the seasoning into the meat and refrigerate if you’re not cooking imminently.
When you’re ready to cook the chicken, bring it out of the fridge to come to room temperature. Heat the oven to 450 Fahrenheit.
Slice the onion in half and peel off the skin, then slice as thinly as you can into half rounds. Place the sliced onion in an 11 x 15-inch (or thereabouts) roasting or sheet pan. Follow this with one lemon: slice the tip and butt off the lemon, then cut it in half lengthwise. Facing the lemon cut-side down, slice it as thinly as possible—these slices really need to be delicate so they can melt. Use a mandolin if you prefer. Get rid of any pips and place the lemon in the pan.
Slice the garlic cloves thinly and add them to the pan, too. Cut the remaining lemon in half and squeeze the juice over everything. Follow with a tablespoon of olive oil and toss to coat.
Pour the chicken and its marinade over the lemon and onions. Attend to each thigh: remove fatty pockets on the underside and detach any skin below the chicken, pulling it outwards. Place each thigh skin-up and splay excess skin so it rests on top of the lemon and onions.
Lay a double-sheet of paper towels on top of the thighs and press to wick away any moisture. Flip the paper and press again, discard. Drizzle the remaining tablespoon of olive oil over the dry chicken.
Bake, uncovered, until the thighs are cooked through, the skin is golden, and the lemon and onion have melted, about 45 minutes. If your thighs are cooked but the skin needs a little encouragement, turn the broiler on high and stand by, inspecting the thighs every couple of minutes until there are enough bubbly bits to get you excited.
Remove the chicken from the oven and taste the sauce before adding the fresh oregano. If you prefer more oregano flavor, sprinkle it into the sauce. The heat from the pan will keep the herb vibrant and help it infuse. Add the capers next and let the chicken rest for a few minutes before serving.
