  We study the nature of constraints and the Hamiltonian structure in a
scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza
and Vernizzi (GLPV). For the simple case with A_5 = 0, namely when the
canonical momenta conjugate to the spatial metric are linear in the extrinsic
curvature, we prove that the number of physical degrees of freedom is three at
fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends
Horndeski's scalar-tensor gravity theory, it is protected against additional
degrees of freedom.
