The J=2-1 and 3-2 rotational lines of the rare isotopomer C36S and the J=5-4 and 6-5 transitions of Si36S were detected in the carbon star IRC+10216 (CW Leo). These are the first detections of 36S bearing molecules in a star and the first spectroscopic detection of Si36S. From a comparison of 34S and 36S bearing isotopomers, th 34S/36S isotopic ratio is 107(+-15). This value is comparable to values in the interstellar medium of the inner Galactic disk (115) but is smaller than the solar value of 288 (Ding et al. 2001). The increase of the 36S abundance relative to 34S only qualitatively follows model predictions of a low mass AGB star. Quantitative agreement of the observed 34S/36S ratio with the stellar models can be reached if the age of IRC+10216 and Galactic chemical evolution are taken into account. Other less likely possibilities are the presence of considerable inhomogeneities in the interstellar medium and either IRC+10216 or the Sun started with a peculiar 36S abundance. Other production mechanisms potentially capable of enhancing the Galactic interstellar medium are discussed. From the observed line density toward IRC+10216 and toward Galactic star forming regions, we estimate the confusion limit toward those sources.