The heavy-fermion metal YbRh 2 Si 2 is a weak antiferromagnet below T N = 0.07 K. Application of a low magnetic field B c = 0.06 T (c) is sufficient to continuously suppress the antiferromagnetic (AF) order. Below T 10 K, the Sommerfeld coefficient of the electronic specific heat γ(T) exhibits a logarithmic divergence. At T < 0.3K, γ(T) ~ T -ε (ε: 0.3 -0.4), while the electrical resistivity ρ(T) = ρ 0 + aT (ρ 0 : residual resistivity). Upon extrapolating finite-T data of transport and thermodynamic quantities to T = 0, one observes (i) a vanishing of the "Fermi surface crossover" scale T*(B), (ii) an abrupt jump of the initial Hall coefficient R H (B) and (iii) a violation of the Wiedemann Franz law at B = B c , the field-induced quantum critical point (QCP). These observations are interpreted as evidence of a critical destruction of the heavy quasiparticles, i.e., propagating Kondo singlets, at the QCP of this material.