Heat oven to 425 degrees and, if you like, line a sheet pan with parchment paper or Silpat liner (not essential but helpful for cleaning up).
Trim the ends off 1 lemon, then cut the lemon in half crosswise.Thinly slice one half of the lemon into rounds, then cut the rounds into quarters, creating small triangles. Shake out the seeds then place the lemon quarters into a large bowl. Save the remaining lemon half for serving. Cut the remaining whole lemon into wedges, for serving.
Add chicken and potatoes to the large bowl with the lemon quarters. Add the oregano, salt and pepper; toss well. (Your hands are the best tools here.) Drizzle in the oil and toss again.
Arrange chicken thighs skin side up on one half of the prepared sheet pan, and potatoes and lemons on the other, spreading the potatoes out into one layer. Roast for 20 minutes. Using a long-handled spoon, stir the potatoes, then spread them out again in one layer. (You don’t have to touch the chicken.) Continue roasting until chicken and potatoes are cooked through and everything is golden and crisped, another 15 to 20 minutes (40 to 45 minutes total roasting time).
To serve, squeeze the juice from the lemon half all over chicken and potatoes and give everything a good stir to incorporate all the tasty juices and browned bits at the bottom of the pan. Sprinkle with more oregano and salt, and serve with additional lemon wedges and condiment dipping sauces on the side, if desired.
{"Note"=>"You can substitute 1¼ pounds chicken drumsticks for the thighs, or use a combination of thighs and drumsticks. Bone-in, skin-on breasts can also be substituted; because they cook more quickly than dark meat does, you’ll need to start checking on them after 30 minutes of total roasting time."}
When I make this dish, I adjust the lemon, oregano, salt and pepper amounts to the total weight I have of chicken and potatoes, especially if the weights of potatoes and chicken aren't equal, as the recipe calls for.