1. Adjust oven rack to lower-middle position and heat oven to 350 degrees. Combine ¾ cup broth, rice, and ¼ teaspoon salt in medium bowl and microwave, covered, until liquid is absorbed, 6 to 8 minutes.
2. Meanwhile, pat chicken dry with paper towels and season with salt and pepper. Heat oil in medium saucepan over medium-high heat until just smoking. Cook chicken until browned all over, about 10 minutes; transfer to plate.
3. Pour off all but 1 teaspoon fat from pot, add onion and ¼ teaspoon salt, and cook over medium-low heat until softened and lightly browned, about 5 minutes. Add garlic and thyme and cook until fragrant, about 30 seconds. Add remaining ½ cup broth and wine, scraping bottom of pot to loosen any browned bits. Stir in parcooked rice, breaking up any large clumps, and bring to simmer. Place chicken skin side up on rice, cover, and bake until rice is cooked through and chicken registers 175 degrees, about 25 minutes.
4. Remove pot from oven, transfer chicken to platter, and tent loosely with aluminum foil. Fluff rice with fork, cover, and let sit for 10 minutes. Stir parsley into rice and season with salt and pepper to taste. Serve rice with chicken.
TIP:Chicken and rice is usually made in a wide skillet. But with such a big circumference, even a covered skillet lets too much steam escape. We had better results with a saucepan, which has a smaller circumference, and hence keeps the moisture where you want it: in with the chicken and rice.