1. Trim excess fat from chicken thighs. Season both sides with salt and pepper.
2. Melt butter with oil in a large skillet over medium heat. When foam subsides, cook chicken until browned and cooked through, turning often, 10 to 12 minutes total. Work in batches and adjust heat if necessary to prevent scorching. Transfer to a plate and cover loosely with foil to keep warm.
3. Pour off all but 1 Tbsp. fat from skillet. Add shallot and cook, stirring, until slightly softened, about 1 minute. Pour in broth and bring to a boil, scraping up any browned bits, until liquid has reduced by half, about 2 minutes. Pour in cream and boil until reduced by half, stirring often, about 3 minutes. Stir in grapes and orange zest. Cook, stirring, until grapes have softened and warmed through and sauce has thickened, about 3 minutes. Season with salt and pepper.
4. Arrange 2 thighs on each of 4 plates and spoon sauce on top. Serve immediately.