  By means of ac magnetic-susceptibility measurements, we find evidence for a
new magnetic phase of Tb$_2$Ti$_2$O$_7$ below about 140 mK in zero magnetic
field. In magnetic fields parallel to [111], this phase---exhibiting frequency-
and amplitude-dependent susceptibility and an extremely slow spin
dynamics---extends to about 70 mT, at which it gives way to another phase. The
field dependence of the susceptibility of this second phase, which extends to
about 0.6 T, indicates the presence of a weak magnetization plateau below 50
mK, as has been predicted by a single-tetrahedron four-spin model, giving
support to the underlying proposal that the disordered low-field ground state
of Tb$_2$Ti$_2$O$_7$ is a quantum spin ice.
