  We have analyzed Atacama Large Millimeter/submillimeter Array Band 6 data of
the hyper-compact H$_{\rm {II}}$ region G24.78+0.08 A1 (G24 HC H$_{\rm {II}}$)
and report the detection of vibrationally-excited lines of HC$_{3}$N
($v_{7}=2$, $J=24-23$). The spatial distribution and kinematics of a
vibrationally-excited line of HC$_{3}$N ($v_{7}=2$, $J=24-23$, $l=2e$) are
found to be similar to the CH$_{3}$CN vibrationally-excited line ($v_{8}=1$),
which indicates that the HC$_{3}$N emission is tracing the disk around the G24
HC H$_{\rm {II}}$ region previously identified by the CH$_{3}$CN lines. We
derive the $^{13}$CH$_{3}$CN/HC$^{13}$CCN abundance ratios around G24 and
compare them to the CH$_{3}$CN/HC$_{3}$N abundance ratios in disks around
Herbig Ae and T Tauri stars. The $^{13}$CH$_{3}$CN/HC$^{13}$CCN ratios around
G24 ($\sim 3.0-3.5$) are higher than the CH$_{3}$CN/HC$_{3}$N ratios in the
other disks ($\sim 0.03-0.11$) by more than one order of magnitude. The higher
CH$_{3}$CN/HC$_{3}$N ratios around G24 suggest that the thermal desorption of
CH$_{3}$CN in the hot dense gas and efficient destruction of HC$_{3}$N in the
region irradiated by the strong UV radiation are occurring. Our results
indicate that the vibrationally-excited HC$_{3}$N lines can be used as a disk
tracer of massive protostars at the HC H$_{\rm {II}}$ region stage, and the
combination of these nitrile species will provide information of not only
chemistry but also physical conditions of the disk structures.
