Raman optical activity (ROA) enables label-free detection of absolute configuration, conformation, and stereochemical structure in chiral biosamples and drug molecules. Since ROA signals are generally small, techniques such as stimulation by a probe beam can be used to enhance signal strength. However, with a classical probe, the measurement precision is still fundamentally limited by its shot noise. To address this limitation, we propose the use of two-mode squeezed vacuum and show that it can achieve sub-shot-noise limited measurement sensitivity. Using quantum estimation theory, we derive the quantum Fisher information and the quantum Cramér-Rao bound (QCRB) for stimulated ROA measurement to quantify the precision enhancement. This improvement comes from photon-number correlations, which suppress the intensity fluctuation common to both modes. We further show that balanced detection of the output intensity difference is a practical measurement scheme that approaches the QCRB and becomes nearly optimal in the small-chirality limit. This opens a promising path toward more sensitive Raman chiroptical spectroscopy of weak and photosensitive samples.