The rotational spectrum of a pure silicon cluster, the Si-3 trimer, has been observed for the first time. From the rotational constants of the normal and the Si-29 and Si-30 isotopic species, a precise geometrical structure has been derived: the trimer is an isosceles triangle with a bond to the apex Si of length 2.177(1) Angstrom and an apex angle of 78.10(3)degrees. The substantial inertial defect and fairly large centrifugal distortion suggest that the molecule possesses a shallow bending potential. Si-3 is a good candidate for astronomical detection because radio lines of comparably massive silicon molecules (e.g., SiC2, SiC4, and SiS) are readily observed in at least one astronomical source. The rotational spectra of Si-6, Si-9, and even larger polar silicon clusters may be detectable with the present technique, as well as similar germanium clusters.