  With the ultimate goal of developing a pixel-based readout for a TPC at the
ILC, a GridPix readout system consisting of one Timepix3 chip with an
integrated amplification grid was embedded in a prototype detector. The
performance was studied in a testbeam with 2.5 GeV electrons at the ELSA
accelerator in Bonn. The error on the track position measurement both in the
drift direction and in the readout plane is dominated by diffusion. Systematic
uncertainties are limited to below 10 $\mu$m. The GridPix can detect single
ionization electrons with high efficiency, which allows for energy loss
measurements and particle identification. From a truncated sum, an energy loss
(dE/dx) resolution of 4.1% is found for an effective track length of 1 m. Using
the same type of chips, a Quad module was developed that can be tiled to cover
a TPC readout plane at the ILC. Simulation studies show that a pixel readout
can improve the momentum resolution of a TPC at the ILC by about 20%.
