The cluster of galaxies A1795 hosts a 46 kpc long filament at its core, which is clearly visible in the light of Hα and X-ray emission. We present optical slit spectroscopy and deeper Chandra X-ray data of the filament. The optical spectra reveal that the bulk of the filament is quiescent (with σ < 130 km s-1), although considerable velocity structure is apparent around the powerful radio source in the central cluster galaxy, where a direct interaction is occurring between the radio plasma and the surrounding intracluster medium. The filament contains a clump of ultraviolet/blue continuum halfway along its length, which we resolve into a chain of at least five distinct knots using archival Hubble Space Telescope images; the optical spectrum of this clump confirms it to be mostly composed of O stars. It is well-removed from the central galaxy and radio source, and is most likely an example of a group of young star clusters condensing directly from the cooling gas in the filament. The observed spatial offset between these knots of star formation and the peak in the optical line emission confirms that the massive star formation is most unlikely to be responsible for the bulk of the observed emission-line luminosity in the filament. Some other (as yet undetermined) source of energy is required to power and maintain the optical line emission, yet it must not completely impede the cooling of the X-ray gas within the filament to form the star clusters.