Transport in ultrathin graphite grown on silicon carbide is dominated by the electron-doped epitaxial layer at the interface. Weak antilocalization in 2D samples manifests itself as a broad cusplike depression in the longitudinal resistance for magnetic fields 10 mT<B<5 T. An extremely sharp weak-localization resistance peak at B=0 is also observed. These features quantitatively agree with graphene weak-(anti)localization theory implying the chiral electronic character of the samples. Scattering contributions from the trapped charges in the substrate and from trigonal warping due to the graphite layer on top are tentatively identified. The Shubnikov-de Haas oscillations are remarkably small and show an anomalous Berry's phase.