We report initial results from our study of the masses and decay constants of the lightest multiplet of charmonium-like hybrid mesons. We obtain precise measurements of the $1^{-+}$ state through the use of a variational basis and a large number of configurations at three lattice spacings. We use staggered fermion operators using configurations generated with the HISQ action with 2+1+1
dynamical flavours. The mixing of the vector hybrid with the $J/\psi$ is examined and a preliminary bound on the vector hybrid decay constant is presented.