Recently, there has been much interest in the use of higher-order spatial clustering statistics, such as N-Point Correlation Functions (NPCFs), to extract cosmological information from the large-scale distribution of galaxies. An NPCF characterizes the excess over random in the spatial clustering of sets of N galaxies at a time. When performing an analysis with NPCFs, one must obtain the inverse covariance matrix to constrain the measurements made. The covariance matrix is typically computed purely from mock galaxy catalogs; however, for analyses with a large number of degrees of freedom, one cannot directly estimate an invertible covariance matrix this way. To better understand the structure of the covariance matrix and pave the way for estimation of it in future analyses, we seek a fully analytic covariance matrix template. I will present a closed-form solution for the covariance matrix of the 2PCF, as well as closed-form solutions for the fundamental building blocks of the covariance matrices of the 3PCF, 4PCF, and beyond. I will then demonstrate how these analytic results may be applied to studies of parity violation in large-scale structure, where there is growing concern that recent detections of parity violation are artifacts of misestimating the covariance matrix. As a robust detection of parity violation will significantly influence the direction of research into the inflationary epoch, it is crucial to ensure that accurate covariance matrices are used in such analyses.