A new highly selective first level ATLAS muon trigger with MDT chamber data for HL-LHC Felix Mueller Max-Planck-Institut fuer Physik, Munich Highly selective first level triggers are essential for the physics programme of the ATLAS experiment at the HL-LHC where the instantaneous luminosity will exceed the LHC's instantaneous luminosity by almost an order of magnitude. The ATLAS first level muon trigger rate is dominated by low momentum sub-trigger threshold muons due to the poor momentum resolution at trigger level caused by the moderate spatial resolution of the resistive plate and thin gap trigger chambers. This limitation can be overcome by including the data of the precision muon drift tube chambers in the first level trigger decision. This requires the implementation of a fast MDT read-out chain and a fast MDT track reconstruction. A hardware demonstrator of the fast read-out chain was successfully tested under HL-LHC operating conditions at CERN's Gamma Irradiation Facility. It could be shown that the data provided by the demonstrator can be processed with a fast track reconstruction algorithm on an ARM CPU within the 6 microseconds latency of the first level ATLAS trigger anticipated for the HL-LHC. The algorithm was also applied to ATLAS LHC run I data to prove under realistic operating conditions that first level single muon trigger rates as low as the high level trigger rates can be achieved with the new MDT based muon trigger.