Type IIn supernovae (SNe) show spectral evidence for strong interaction between their blast wave and dense circumstellar material (CSM) around the progenitor star. SN 2010jl was the brightest core-collapse supernova in 2010, and it was a Type IIn explosion with strong CSM interaction. Andrews et al. recently reported evidence for an infrared (IR) excess in SN 2010jl, indicating either new dust formation or the heating of CSM dust in an IR echo. Here we report multi-epoch spectra of SN 2010jl that reveal the tell-tale signature of new dust formation: emission-line profiles becoming systematically more blueshifted as the red side of the line is blocked by increasing extinction. The effect is seen clearly in the intermediate-width (400-4000 km s −1 ) component of Hα beginning roughly 30 days after explosion. Moreover, we present near-IR spectra demonstrating that the asymmetry in the hydrogen-line profiles is wavelength dependent, appearing more pronounced at shorter wavelengths. This evidence suggests that new dust grains had formed quickly in the post-shock shell of SN 2010jl arising from CSM interaction. Since the observed dust temperature has been attributed to an IR echo and not to new dust, either (1) IR excess emission at λ < 5 μm is not a particularly sensitive tracer of new dust formation in SNe, or (2) some assumptions about expected dust temperatures might require further study. Lastly, we discuss one possible mechanism other than dust that might lead to increasingly blueshifted line profiles in SNe IIn, although the wavelength dependence of the asymmetry argues against this hypothesis in the case of SN 2010jl.