We consider the entanglement entropy of a free massive scalar field in the one parameter family of *α*-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An *α*-vacuum can be thought of as a state filled with particles from the point of view of the Bunch-Davies vacuum. Of all the *α*-vacua we find that the entanglement entropy takes the minimal value in the Bunch-Davies solution. We also calculate the asymptotic value of the Rényi entropy and find that it increases as *α* increases. We argue these features stem from pair condensation within the non-trivial *α*-vacua where the pairs have an intrinsic quantum correlation.