Stir together paprika and oregano. Arrange chicken on a large rimmed baking sheet and season with 2 tablespoons salt, then the spice mixture (use all of it). Set aside at room temperature (or refrigerate chicken, uncovered, overnight).
Preheat the oven to 325 degrees. Drain tomatoes and tear them into 4 or 6 strips each, transferring to another large rimmed baking sheet as you go. Drain and rinse chickpeas; add to baking sheet. Add the thyme, bay leaves, and chiles, scattering them about. Season with salt and pepper, then pour over ½ cup oil and stir to coat. Bake until tomatoes are shrunken and look a bit dried out, and chickpeas are starting to turn golden brown, 1 hour, stirring once halfway through (this cooks off some moisture in the tomatoes so they’ll get nice and jammy by the end).
Meanwhile, peel the onion and cut into ¼-inch wedges. Lightly crush the garlic cloves. Add the onion and garlic to tomato-chickpea mixture. Nestle in chicken, skin side up, then pour over the remaining ¾ cup oil. Bake until the skin is browned and the meat is tender enough to shred with a fork, 1½ hours. If chicken isn’t done, bake for 15 minutes more, then check again. Go longer if needed.
Transfer chicken to a large platter. Pluck out bay leaves and thyme sprigs. Using a slotted spoon, spoon tomatoes and chickpeas around chicken. Pour cooking liquid from baking sheet into a glass measuring cup; let settle for a few minutes. Pour most of the oil that rises to the top of the liquid into a clean jar or bowl, then spoon remaining chicken-y juices over the platter. (Cover and refrigerate the extra confit oil; use it the next time you make beans, soup, or roast vegetables.) Season the chicken with a few dashes of vinegar before serving.
