Combine the ingredients for the marinade in a zip-top bag. Trim as much fat as practical from the chicken thighs and add to the bag. Allow to marinate from 1 hour to overnight.
Preheat oven to 350 degrees F. Remove chicken from marinade and pat dry. Remove garlic and discard; reserve the remainder of the marinade.
In a deep, heavy-bottomed skillet or Dutch oven, warm 2 tbsp of the olive oil over medium-high heat. Add the chicken thighs, skin side down. Cook until golden brown, about 5 minutes, then flip and cook the other side until golden-brown, about 5 minutes more. Reduce heat to medium-low; remove chicken to a plate and reserve.
Wipe excess fat from the pan, then add the remaining olive oil. Add the shallots and saute 1 minute. Add the rice, lemon zest, capers, herbs, and a generous pinch of salt; saute until rice is translucent and fragrant, about 2 minutes. Carefully add the wine and stir until absorbed, scraping any brown bits from the bottom of the pan.
Add the marinade and broth; bring to a simmer. Allow to simmer for about 30 seconds. Arrange the chicken on top of the rice, skin side up. (The dish will be quite soupy at this point and the chicken will be partially submerged. No worries! The rice will absorb it all!) Pour any accumulated juices over the top. Arrange lemon slices on top of the chicken and rice.
Lid the skillet and place in the oven. Bake for 35 minutes. Remove the lid and bake an additional 10 minutes (45 in total), or as necessary until the chicken is cooked through (165 degrees F), liquid is absorbed, and the rice is tender.
Remove from the oven and allow to rest for 10 minutes. Serve garnished with parsley. Enjoy!