Heat oven to 425° F. Toss the parsnips, honey, 1 tablespoon of the oil, and ½ teaspoon each salt and pepper on a rimmed baking sheet. Roast, tossing occasionally, until golden brown, 30 to 35 minutes.
Meanwhile, heat the remaining 1 tablespoon of oil in a large skillet over medium-high heat. Season the chicken with ¼ teaspoon each salt and pepper and brown in batches, 4 to 6 minutes per side. Transfer to a rimmed baking sheet; reserve the skillet. Roast the chicken in oven until an instant-read thermometer inserted in the thickest part of a thigh registers 165° F, 5 to 7 minutes for small thighs and 12 to 15 minutes for large ones.
Add the raisins, vinegar, ¼ teaspoon salt, and ½ teaspoon pepper to the drippings in the skillet and cook, scraping up the bits stuck to the pan, until the vinegar is reduced by half, 30 to 45 seconds. Add the collard greens and cook, stirring, until wilted, 1 to 2 minutes. Serve with the chicken and parsnips.