We study nonequilibrium transport through a charge Kondo device realizing the two-channel Kondo critical point in a recent experiment by Iftikhar et al . By computing the current and shot noise at low voltages near the critical point, we obtain a universal Fano factor of 1/2. We identify elementary transport processes as weak scattering of emergent fermions carrying half-integer charge quantum numbers. This forms an experimental fingerprint for fractionalization in a nonFermi liquid, which, compared to spin-Kondo devices, could be observed at elevated temperatures