The beam spectrometer of the NA62 experiment, named Gigatracker, has to perform single track reconstruction with unprecedented time resolution (150 ps rms) in a harsh radiation environment. To meet these requirements, and in order to reduce material budget to a minimum, three hybrid silicon pixel detector stations will be installed in vacuum. An adequate strategy to compensate for the discriminator time-walk must be implemented and R&D investigating two different options is ongoing. Two read-out chip prototypes have been designed in order to compare their performance: one approach is based on the use of a constant-fraction discriminator followed by an on-pixel TDC, while the other one is based on the use of a time-over-threshold circuit followed by a TDC shared by a group of pixels. This paper describes the Gigatracker system, presents the global architectures of both read-out ASICs and reviews the current status of the R&D project.