By means of ac magnetic-susceptibility measurements, we find evidence for a new magnetic phase of Tb2Ti2O7 below about 140 mK in zero magnetic field. In magnetic fields parallel to [111], this phase is characterized by frequency- and amplitude-dependent susceptibility and extremely slow spin dynamics. In the zero-temperature limit, it extends to about 67 mT (the internal field H(int)≃52 mT), at which it makes transition to another phase. The field dependence of the susceptibility of this second phase, which extends to about 0.60 T (H(int)≃0.54 T) in the zero-temperature limit, indicates the presence of a weak magnetization plateau below about 50 mK, as has been predicted by a single-tetrahedron four-spin model, suggesting that the second phase is a quantum kagome ice.