In a large skillet, heat the oil until shimmering. Add the chicken livers and cook over high heat until lightly browned on the bottoms, about 2 minutes. Turn the livers. Add the shallot, garlic and thyme to the skillet and cook until the shallot and garlic are fragrant and softened, about 2 minutes. Add the sherry and cook, scraping up any bits stuck to the bottom of the pan, until the liquid is evaporated and the livers are cooked through, about 2 minutes. Scrape the mixture into a food processor and pulse until chopped. With the machine on, add the butter and puree until smooth. Scrape the chicken-liver butter into a bowl and season with salt and pepper.