Thinking that Parker has inherited big money from his great-aunt, Binghamton signs a deal with a crooked Frenchman, to buy some supposedly valuable real estate on New Caledonia, and McHale and the crew try to help him get out of the situation.

Binghamton's niece Cynthia arrives and is intrigued by Parker's resemblance to the Missing Link. Binghamton mistakenly assumes that she plans to marry Parker, and chaos ensues.