A measurement of the pp --> p p eta reaction at the excess energy of Q = 15.5 +- 0.4 MeV has been carried out at the internal beam facility COSY-11 with an integrated luminosity of 811 nb^-1 The number of ~24000 identified events permits a precise determination of total (2.32 +- 0.05 +- 0.35 mu b) and differential cross sections. Preliminary investigations show that the angular distribution of the eta meson in the center-of-mass system is isotropic. A qualitative analysis of the Dalitz-plot distribution is presented.