Crystal structure, specific heat, thermal expansion, magnetic susceptibility and electrical resistivity studies of the heavy fermion system CeNi_{9-x}Cu_xGe_4 (0 <= x <= 1) reveal a continuous tuning of the ground state by Ni/Cu substitution from an effectively fourfold degenerate non-magnetic Kondo ground state of CeNi_9Ge_4 (with pronounced non-Fermi-liquid features) towards a magnetically ordered, effectively twofold degenerate ground state in CeNi_8CuGe_4 with T_N = 175 +- 5 mK. Quantum critical behavior, C/T ~ chi ~ -ln(T), is observed for x about 0.4. Hitherto, CeNi_{9-x}Cu_xGe_4 represents the first system where a substitution-driven quantum phase transition is connected not only with changes of the relative strength of Kondo effect and RKKY interaction, but also with a reduction of the effective crystal field ground state degeneracy.
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