Vortex-carrying matter waves, such as chiral electron beams, are of significant interest in both applied and fundamental science. Continuous-wave electron vortex beams are commonly prepared via passive phase masks imprinting a transverse phase modulation on the electron's wavefunction. Here, we show that femtosecond chiral plasmonic near fields enable the generation and dynamic control on the ultrafast timescale of an electron vortex beam. The vortex structure of the resulting electron wavepacket is probed in both real and reciprocal space using ultrafast transmission electron microscopy. This method offers a high degree of scalability to small length scales and a highly efficient manipulation of the electron vorticity with attosecond precision. Besides the direct implications in the investigation of nanoscale ultrafast processes in which chirality plays a major role, we further discuss the perspectives of using this technique to shape the wavefunction of charged composite particles, such as protons, and how it can be used to probe their internal structure.