Molecular chirality, a geometric property of utmost importance in biochemistry, is now being investigated in the time-domain. Ultrafast chiral techniques can probe the formation or disappearance of stereogenic centers in molecules. The element-sensitivity of X-rays adds the capability to probe chiral nuclear dynamics locally within the molecular system. However, the implementation of ultrafast techniques for measuring transient chirality remains a challenge because of the intrinsic weakness of chiral-sensitive signals based on circularly polarized light. We propose a novel approach for probing the enantiomeric dynamics by using the orbital angular momentum (OAM) of X-ray light, which can directly monitor the real-time chirality of molecules. Our simulations probe the oscillations in excited chiral formamide on different potential energy surfaces and demonstrate that using the X-ray OAM can increase the measured asymmetry ratio. Moreover, combining the OAM and SAM (spin angular momentum) provides stronger dichroic signals than linearly polarized light, and offers a powerful scheme for chiral discrimination.