We present the high-resolution (11 MHz) infrared measurement of the molecular Stark effect for the R(0) transition of the acetylenic C-H stretch in 2-propyn-1-ol. The field-free spectrum is fragmented into three eigenstate components due to the effects of intramolecular vibrational energy redistribution (IVR). As the field strength increases from 0 to 25 kV/cm, the number of eigenstates increases linearly. The center-of-gravity of the fragmented R(0) transition follows the simple, second-order Stark shift (Delta v alpha E(2)) expected for the bright state. However, when viewed at the eigenstate level, the mechanism of the Stark shift is rather complex. At lower field strengths, the eigenstates shift in energy, as occurs for Stark effects in lower state density regimes. As the number of coupled states increases, energy shifting of the eigenvalues is quenched. To preserve the second-order Stark shift of the center-of-gravity, the intensity "rolls over" the largely rigid eigenvalue structure. For molecules in regions of high state density, the reduced energy shifting of the eigenvalues as the electric field is increased means that lack of deflection by inhomogeneous electric fields is not necessarily a consequence of the molecule being nonpolar.