We present observations of CO overtone bandhead emission toward four massive Young Stellar Objects ( spectral type O6–B5 ) . The high signal-to-noise ratio K -band spectra were obtained with VLT-ISAAC at a resolution \Delta v = 30 km s ^ { -1 } , sufficient to resolve the bandheads , but not the individual J -lines . We are able to explain the shape of the lines by assuming a simple isothermal keplerian disk model seen at different inclinations . The gas temperature ranges from 1500 to 4500 K and the CO column density is between 0.1 and 4 \times 10 ^ { 21 } cm ^ { -2 } . The emission probably arises within the first few astronomical units of the disk , consistent with the high gas temperature . Our results indicate that molecules can survive close to a hot star and suggest that dense ( n _ { H } > 10 ^ { 10 } cm ^ { -3 } ) inner disks may be relatively common at an advanced stage of high-mass star formation .