Carrier mobility is one of the most important parameters of any semiconductor material, determining its suitability for applications in a large variety of electronic devices including field effect transistors (FETs). Today the capabilities of modern planar Si PET devices are almost exhausted and researchers are seeking either new device architectures or new materials. Here we report an extremely high room temperature (at 293 K) 2D hole gas (2DHG) drift mobility of 4500 cm(2) V-1 s(-1) at a carrier density of 1.2 x 10(11) cm(-2) obtained in a compressively strained Ge quantum well (QW) heterostructure, grown by an industrial type chemical vapor deposition system on a standard Si(001) substrate. The low-temperature Hall mobility and carrier density of this structure, measured at 333 mK, are 777,000 cm(2) V-1 s(-1) and 1.9 x 10(11) cm(-2), respectively. These hole mobilities are the highest not only among the group-IV Si and Ge based semiconductors, but also among p-type III-V and II-VI materials. The obtained room temperature mobility is substantially higher than those reported so far in strained Ge QW heterostructures and reveals a huge potential for further applications of this material in a wide variety of electronic devices. (C) 2015 Elsevier Ltd. All rights reserved.