A chiller system includes a mechanical-cooling circuit configured to circulate a refrigerant through an evaporator of the mechanical-cooling circuit, where the evaporator is configured to cool a conditioning fluid with the refrigerant. The chiller system also includes a free-cooling circuit configured to circulate the refrigerant through a heat exchanger of the free-cooling circuit, where the heat exchanger is configured to cool the conditioning fluid with the refrigerant. The chiller system also includes a distribution header having a first inlet configured to receive the refrigerant from the mechanical-cooling circuit, a second inlet configured to receive the refrigerant from the free-cooling circuit, and an internal volume fluidly coupled to the first inlet and the second inlet. A fan coil unit of the chiller system is configured to receive the refrigerant from the internal volume of the distribution header.