Wireless communication at millimeter wave frequencies is an attractive option for high-bit-rate connectivity to unmanned aerial vehicles (UAVs). However, conducting the channel measurements necessary to assess the communication performance at these frequencies has been challenging due to the severe payload and power restrictions in commercial UAVs. This work presents a novel lightweight (approximately 1.3kg) channel measurement system at 28GHz installed on a commercially available UAV. A ground transmitter equipped with a horn antenna conveys sounding signals to a UAV equipped with a lightweight spectrum analyzer. We demonstrate that the measurements can be highly influenced by the onboard antenna pattern as shaped by the UAV's frame. A calibration procedure is presented to correct for the resulting angular variations in antenna gain. The measurement setup is then validated on real flights from an airstrip at distances in excess of 300m.