We demonstrate nonlinear temporal compression of a vortex beam by propagation in a gas-filled capillary. Starting from an ytterbium-based laser delivering 700 μJ 640 fs pulses at a 100 kHz repetition rate, the vortex beam is generated using a spiral phase plate and coupled to a capillary where it excites a set of four modes that have an overlap integral of 97% with a Laguerre-Gauss LG10 mode. Nonlinear propagation of this hybrid, orbital angular momentum (OAM)-carrying mode results in temporal compression down to 74 fs at the output. Beam and pulse characterizations are carried out to determine the spatial profile and temporal duration of compressed pulses. This result in multimode nonlinear optics paves the way towards the generation of OAM-carrying few-cycle pulses, isolated attosecond XUV pulses, and tunable UV pulses through resonant dispersive wave emission.