This was first printed in the 4th edition of Playford's The English Dancing Master (1670) and was retained through the 8th edition of 1690. The Lord Chamberlain or Lord Chamberlain of the Household is the senior officer of the Royal Household of the United Kingdom, overseeing the departments which support and provide advice to the Sovereign. The Lord Chamberlain is always sworn of the Privy Council, is usually a peer and before 1782 the post was of Cabinet rank. The position was a political one until 1924. The office dates from the Middle Ages when the King's Chamberlain often acted as the King's spokesman in Council and Parliament. In the years preceding the first printing in 1670 the Lords Chancellor were the Earls of Essex, Dorset and, during the interregnum, Baronet Sir Gilbert Pickering. At the restoration of the monarchy, The Earl of Manchester held the title.
I can't determine if the title "The Lord Chamberlain's Delight" refers to a specific person or is just a general reference.