This paper investigates spillover effects of house supply on nearby house prices across the housing cycle. Over the past five years, housing inventory shortages have been a primary factor in rising house prices. At the same time, demand for housing has risen aggressively as the job market has improved and millennials are aging into homeownership. The combination of limited homes on the market with high buyer demand has pushed house prices above what they were at the peak of the housing boom in early 2006. The underlying reasoning behind this idea - low supply should lead to price increases - is clear and some influential research has strongly suggested the inverse relationship by applying matching models to the housing market. However, there is a surprising lack of empirical work done on this inverse relationship, in particular, at the level of the local housing market. Furthermore, no empirical research has addressed the role of spatial spillovers between different regions in the relationship. Using a spatial panel model for 77 community areas within the Chicago area between 2009 and 2018, the study shows substantial asymmetric spatial effects; for instance, how the nearby house supply can serve as a key determinant on house prices in a boom period. However, these effects may not hold during market downturn.