Add the marinade ingredients (lemon juice, olive oil, garlic, and rosemary) to a small bowl. Stir to combine. Set aside.
Wash and thoroughly dry the chicken. Salt both sides of each chicken thigh.
Lay the chicken thighs out in a single layer in a 9” x 11” dish. Pour the marinade over the chicken. Cover with aluminum foil or saran wrap. Refrigerate while marinating for 2 – 3 hours.
Heat a large heavy-bottomed skillet over medium heat. Once the skillet is heated, add oil and swirl to coat the pan.
Add chicken, skin side down, to the oiled pan. Cover with a splatter screen. Sauté until the skin is crispy and golden brown and the fat has rendered. This could take up to 30 minutes. Keep an eye on them and turn the temperature down if the skin is starting to blacken. The temperature that you use to sauté the chicken is largely dependent on your element. If your element runs hot, you’ll likely need to sauté the chicken at medium-low, or even low.
Flip each piece and continue to cook until the chicken is cooked through. This can take up to 20 more minutes. The chicken is cooked when the meat closest to the bone measures a minimum of 165 F on a meat thermometer (being sure not to touch the bone with the meat thermometer).
Remove the chicken from the pan and set aside. Drain the excess fat from the skillet, being sure to reserve the flavorful bits at the bottom.
Return skillet to heat and turn heat to low to begin making the sauce. Add the white wine and deglaze the pan, scraping up and mixing in any of the flavorful bits at the bottom of the fry pan. Add in the rosemary, shallots, and garlic. Simmer until the wine is nearly dissolved, stirring about once a minute. Once the wine is mostly dissolved, turn the heat off. Add in the cubed butter a little bit at a time. Stir until the butter is fully melted and incorporated before adding more butter. Once all of the butter is incorporated into the sauce, remove the pan immediately from the stove to stop the residual heat from overcooking the sauce. Taste and add salt, pepper, and optional lemon zest to your taste preference at this point.
Serve immediately. Spoon the sauce onto a plate and serve the chicken on top of the sauce.