A sensitive search for direct CP violation in $\Xi^-$ ($\bar{\Xi}^+$) and $\Lambda$ ($\bar{\Lambda}$) decays is underway at FNAL. Experiment E871 (HyperCP) intends to perform a precision measurement of the angular distribution of protons (anti-protons) with respect to the helicity axis in the rest frame of the $\Lambda \; (\bar{\Lambda})$. The slopes of these distributions give the decay parameters $\alpha_{\Xi}\alpha_{\Lambda}$ and $\alpha_{\bar{\Xi}}\alpha_{\bar{\Lambda}}$. An asymmetry parameter $\mathcal{A}$ in terms of these decay parameters has been defined for which a non-zero value would be unambiguous evidence for direct CP violation. Theoretical predictions for $\mathcal{A}$ range from no asymmetry up to $\sim 10^{-3}$. HyperCP expects to measure $\mathcal{A}$ with an uncertainty of $\sim 2\times 10^{-4}$.