  We report low-temperature calorimetric, magnetic and resistivity measurements
on the antiferromagnetic (AF) heavy-fermion metal YbRh$_2$Si$_2$ (${T_N =}$ 70
mK) as a function of magnetic field $B$. While for fields exceeding the
critical value ${B_{c0}}$ at which ${T_N\to0}$ the low temperature resistivity
shows an ${AT^2}$ dependence, a ${1/(B-B_{c0})}$ divergence of ${A(B)}$ upon
reducing $B$ to ${B_{c0}}$ suggests singular scattering at the whole Fermi
surface and a divergence of the heavy quasiparticle mass. The observations are
interpreted in terms of a new type of quantum critical point separating a
weakly AF ordered from a weakly polarized heavy Landau-Fermi liquid state.
