  We show that there is an essentially unique S-algebra structure on the Morava
K-theory spectrum K(n), while K(n) has uncountably many MU or \hE{n}-algebra
structures. Here \hE{n} is the K(n)-localized Johnson-Wilson spectrum. To prove
this we set up a spectral sequence computing the homotopy groups of the moduli
space of A-infinity structures on a spectrum, and use the theory of S-algebra
k-invariants for connective S-algebras due to Dugger and Shipley to show that
all the uniqueness obstructions are hit by differentials.
