The Pixel Chamber project purpose is the production of the first solid state active target capable of performing continuous, high-resolution (O(μm)) 3D tracking. The aim is to create a bubble chamber-like high-granularity stack of hundreds of very thin monolithic active pixel sensors (MAPS) glued together. In this paper, the R&D to develop the first prototypes with ALPIDE sensors, designed for the ALICE experiment at the CERN LHC, will be presented. Tracking and vertexing algorithms were developed to reconstruct tracks and vertices inside Pixel Chamber. They were tested on Monte Carlo simulations which show that it is possible to obtain a high efficiency for the reconstruction of hadronic tracks, and for the primary and secondary vertices inside the detector. The tracking algorithm has been tested on test beam data to reconstruct long tracks produced in a single ALPIDE sensor parallel to a beam. Results show that it is possible to obtain very good performances in long track reconstruction on a single ALPIDE. Among the possible applications, Pixel Chamber used as an active target, has the potential to allow precision measurements of charm and beauty production. Even more interesting are possible medical and astrophysical applications. The usage of the Pixel Chamber as scatterer detector in Compton Cameras would reduce by orders of magnitude the numbers of gammas required for performing a precise source imaging, both for in vivo monitoring during hadron therapy and for astrophysics measurements.