Performance of the ALICE Time Projection Chamber

The Time Projection Chamber of the ALICE experiment is a large 3-dimensional tracking device for ultra-high multiplicity events. It has been operated successfully at the Large Hadron Collider at CERN, recording collisions of protons (since November 2009) and of heavy-ions (lead nuclei, in November 2010). We describe the detector and the calibration procedures necessary to guarantee an optimal data quality. We report on the performance, in particular of tracking and particle identification, and on readout speed. Finally, we summarize the challenges in the design and the experience in operating the Time Projection Chamber under the extreme conditions of heavy-ion collisions at the LHC.