Recent advances in high speed rails (HSRs), coupled with user demands for communication on the move, are propelling the need for acceptable quality of communication services in high speed mobility scenarios. This calls for an evaluation of how well popular voice/video call applications, such as Skype, can perform in such scenarios. This paper presents the first comprehensive measurement study on Skype voice/video calls in LTE networks on HSRs with a peak speed of 310 km/h in China. We collected 50 GB of performance data, covering a total HSR distance of 39,900 km. We study various objective performance metrics (such as RTT, sending rate, call drop rate, etc.), as well as subjective metrics such as quality of experience of the calls. We also evaluate the efficiency of Skype's algorithms regarding the level of utilization of network resources. We observed that the quality of Skype calls degrades significantly on HSRs. Moreover, it was discovered that Skype significantly under-utilizes the network resources, such as available bandwidth. We discovered that the root of these inefficiencies is the poor adaptability of Skype in many aspects, including overlay routing, rate control, state update and call termination. These findings highlight the need to develop more adaptive voice/video call services for high speed mobility scenarios.