Recent Monte Carlo calculations of the radial distribution function of a one‐component, classical, plasma are shown to be well approximated by solutions of the Born‐Green‐Yvon integral equation, almost up to densities where there is definite short range order. The Born‐Green‐Yvon solutions appear to be somewhat better than the corresponding solutions of the Percus‐Yevick and convolution‐hypernetted‐chain equations. The Born‐Green‐Yvon equation is further shown to be related to the original Debye‐Hu¨ckel equation for an ionic solution. It differs from the latter equation by accounting for more short range correlations, a feature that makes it more accurate at higher densities. The special methods used to obtain numerical solutions of the Born‐Green‐Yvon equation at high density are briefly discussed.