The chairman of Winston & Strawn LLP’s litigation department is leaving to join another large Chicago law firm.James F. Hurst, who is known as a major but low-key rainmaker, joins Kirkland & Ellis LLP as a partner on Monday. He will be a member of its litigation and intellectual property practice groups. Winston is the only firm Hurst, 50, has worked at during his legal career. He could not be reached for comment.Mark R. Filip, a partner at 1,600-lawyer Kirkland, called Hurst “a very experienced …