We present herein a comparison between the areas of solar polar coronal holes and north-south (N-S) cosmic ray asymmetries (as measured by polar region neutron monitors). The observed N-S asymmetries over a 2-year period (1973--1974) are found to be related to asymmetries in the sizes of selected solar polar holes; the hemisphere with the smaller hole has a larger cosmic ray flux. An analysis is also made of the N-S asymmetries for intervals when there exists a relatively symmetric coronal region (¿40 ¿) about the solar equator; the N-S asymmetry tends to be small for this situation of comparable-sized polar coronal holes. We discuss various mechanisms which can contribute to a N-S asymmetry. The radial gradient drift effect (∇n¿B) alone probably cannot explain a N-S asymmetry. The importance of the role of coronal holes in cosmic ray modulation processes as demonstrated in this work is stressed.