All-optical switching increasingly plays an important role in optical information processing. However, simultaneous achievement of ultralow power consumption, broad bandwidth and high extinction ratio remains challenging. We experimentally demonstrate an ultralow-power all-optical switching by exploiting chiral interaction between light and optically active material in a Mach-Zehnder interferometer (MZI). We achieve switching extinction ratio of 20.0(3.8) and 14.7(2.8) dB with power cost of 66.1(0.7) and 1.3(0.1) fJ/bit, respectively. The bandwidth of our all-optical switching is about 4.2 GHz. Our theoretical analysis shows that the switching bandwidth can, in principle, exceed 110 GHz. Moreover, the switching has the potential to be operated at few-photon level. Our all-optical switching exploits a chiral MZI made of linear optical components. It excludes the requisite of high-quality optical cavity or large optical nonlinearity, thus greatly simplifying realization. Our scheme paves the way towards ultralow-power and ultrafast all-optical information processing.