We present spatial coherence measurements of extreme ultraviolet (EUV) light generated through the process of high-harmonic up-conversion of a femtosecond laser. With a phase-matched hollow-fiber geometry, the generated beam was found to exhibit essentially full spatial coherence. The coherence of this laser-like EUV source was shown by recording Gabor holograms of small objects. This work demonstrates the capability to perform EUV holography with a tabletop experimental setup. Such an EUV source, with low divergence and high spatial coherence, can be used for experiments involving high-precision metrology, inspection of optical components for EUV lithography, and microscopy and holography with nanometer resolution. Furthermore, the short time duration of the EUV radiation (a few femtoseconds) will enable EUV microscopy and holography to be performed with ultrahigh time resolution.