A novel form of ion-tracks, namely nanogrooves and hillocks, are observed on CaF2 after irradiation with xenon and lead ions of about 100 MeV kinetic energy. The irradiation is performed under grazing incidence (0.3°-3°) which forces the track to a region in close vicinity to the surface. Atomic force microscopy imaging of the impact sites with high spatial resolution reveals that the surface track consists in fact of three distinct parts: each swift heavy ion impacting on the CaF2 surface first opens a several 100 nm long groove bordered by a series of nanohillocks on both sides. The end of the groove is marked by a huge single hillock and the further penetration of the swift projectile into deeper layers of the target is accompanied by a single protrusion of several 100 nm in length slowly fading until the track vanishes. By comparing experimental data for various impact angles with results of a simulation, based on a three-dimensional version of the two-temperature-model (TTM), we are able to link the crater and hillock formation to sublimation and melting processes of CaF2 due to the local energy deposition by swift heavy ions.