In order to investigate the suppression of the heavy-fermion state of CeCu6 by a magnetic field (B ∥ c) we have measured the coefficients of thermal expansion of a single-crystalline sample (αa, αb, αc) in the temperature range 0.3–10 K in fields up to 8 T. The electronic Grüneisen parameter (Γhf = Vmav/κγ), which amounts to 80 in zero field (T → 0), is reduced by a factor 10 in a field of 8 T. This enormous drop of Γ is attributed to a rapid suppression of the magnetic inter-site correlations.