  A weak perpendicular magnetic field, $B$, breaks the chiral symmetry of each
valley in the electron spectrum of graphene, preserving the overall chiral
symmetry in the Brillouin zone. We explore the consequences of this symmetry
breaking for the interaction effects in graphene. In particular, we demonstrate
that the electron-electron interaction lifetime acquires an anomalous
$B$-dependence. Also, the ballistic zero-bias anomaly, $\delta \nu(\omega)$,
where $\omega$ is the energy measured from the Fermi level, emerges at a weak
$B$ and has the form $\delta\nu(B)\sim B^2/\omega^2$. Temperature dependence of
the magnetic-field corrections to the thermodynamic characteristics of graphene
is also anomalous. We discuss experimental manifestations of the effects
predicted. The microscopic origin of the $B$-field sensitivity is an extra
phase acquired by the electron wave-function resulting from the
chirality-induced pseudospin precession.
