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We have measured the ac nonlinear dielectric response χ3 (ω, T) of an archetypical glassformer (glycerol) just above its glass transition temperature Tg ∼190 K. Our measurements were performed at temperatures between Tg + 4 K and Tg + 35 K, which corresponds to 5 decades of variation of the relaxation time τ (T) of the liquid. We find that χ3(ω, T) is peaked for ωτ ∼ 0.2 and that the height of the peak grows as one approaches Tg. A powerlaw in frequency beyond the peak of χ3 is observed and χ3 (ω, T) displays scaling as a function of ωτ. These features correspond to the main predictions of some recent theoretical works relating the nonlinear susceptibility of supercooled liquids to the average number Ncorr of dynamically correlated molecules. We thus interpret the experimental increase of the peak of nonlinear susceptibility when T decreases, as an increase of Ncorr when T Tg. This strongly reinforces the collective picture of the dynamics of supercooled liquids close to the glass transition. Finally, we discuss some heating effects and show that they do not affect significantly our conclusions. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)