  We calculate the mode-dependent transmission probability of massless Dirac
fermions through an ideal strip of graphene (length L, width W, no impurities
or defects), to obtain the conductance and shot noise as a function of Fermi
energy. We find that the minimum conductivity of order e^2/h at the Dirac point
(when the electron and hole excitations are degenerate) is associated with a
maximum of the Fano factor (the ratio of noise power and mean current). For
short and wide graphene strips the Fano factor at the Dirac point equals 1/3,
three times smaller than for a Poisson process. This is the same value as for a
disordered metal, which is remarkable since the classical dynamics of the Dirac
fermions is ballistic.
