CNES, LKB and SYRTE are developing a primary frequency standard, called PHARAO, which is specially designed for space applications. The clock signal is referenced on the frequency measurement of the hyperfine transition performed on a cloud of cold cesium atoms (~1 µK). The transition is induced by an external field feeding a Ramsey cavity. In microgravity the interaction time inside the cavity can be adjusted over two orders of magnitude by changing the atomic velocity (5 cm·s-1–5 m·s-1) in order to study the ultimate performances of the clock. An engineering model has been assembled to validate the architecture of the clock. This model has been fully tested on ground for operation faults. Of course the clock performances are reduced by the effect of the gravity on the moving atoms. The main results are a frequency stability of 3.3 × 10-13t-1/2. The main systematic effects have been analyzed and their frequency uncertainties contribution is 1.6 × 10-15. The clock has been compared with the primary frequency standard, the mobile fountain of SYRTE. The mean frequency shift is lower than 2 × 10-15. The mechanical and thermal space qualifications have been carried out by testing a representative mechanical model of the clock and by using refined calculations. The design of the clock has been improved and now the flight model is being assembled. The PHARAO clock is a key instrument of the European ESA space mission called ACES. This mission is dedicated to perform space-time measurements in order to test some fundamental physics aspects.