A new method for sizing vertical ground heat exchangers is proposed using topology optimization to reduce the number of boreholes required to fulfill the cooling and heating demand. The ASHRAE sizing equation is adapted to formulate a topology optimization problem to minimize the number of boreholes required in a bore field. The results show that topology optimization can help reduce the number of boreholes required when compared to a sizing performed on a regular grid using conventional sizing methods. These optimized configurations show smaller spacings between the boreholes located on the perimeter and larger spacings between the boreholes located in the center of the bore field.