Recently, there has been much progress in the design and application of oil-repellent superoleophobic surfaces. Polyzwitterionic brush surfaces are of particular interest, because of their ability to repel oil under water, even in the absence of micro-/nanostructures. The origin of this underwater superoleophobicity is attributed to the presence of a stable water film beneath the oil droplet, but this had not been demonstrated experimentally. Here, using optical interferometric techniques, we show that an oil droplet effectively hydroplanes over a water film, whose thickness is between one hundred and hundreds of nanometres. In addition, using a custom-built droplet force apparatus, we find the friction and adhesion forces to be in the nN range for millimetric-sized droplets. These forces are much lower than for other classes of well-known liquid-repellent surfaces, including the lotus-leaf effect and lubricant-infused surfaces, where the typical force is on the order of μN.