We experimentally created a femtosecond optical vortex using a pair of computer-synthesized holographic gratings arranged in a 2f - 2f optical setup. We present measurements showing that the resulting donut mode is free of spatial chirp, and support this finding with an analysis of the optical wave propagation through our system based on the Kirchhoff-Fresnel diffraction integral. An interferogram confirms that our ultrashort vortex has topological charge 1, and a conservative experimental estimation of its duration is 280 fs. We used 25-fs radiation pulses (bandwidth approximately 40 nm) produced by a Ti:sapphire laser oscillator.