We have used the Mopra Telescope to search for glycine and the simple chiral molecule propylene oxide in the Sgr B2 (LMH) and Orion KL, in the 3-mm band. We have not detected either species, but have been able to put sensitive upper limits on the abundances of both molecules. The 3 sigma upper limits derived for glycine conformer I are 3.7 x 10(14) cm(-2) in both Orion-KL and Sgr B2 ( LMH), comparable to the reported detections of conformer I by Kuan et al. However, as our values are 3s upper limits rather than detections we conclude that this weighs against confirming the detection of Kuan et al. We find upper limits for the glycine II column density of 7.7 x 10(12) cm(-2) in both Orion-KL and Sgr B2 ( LMH), in agreement with the results of Combes et al. The results presented here show that glycine conformer II is not present in the extended gas at the levels detected by Kuan et al. for conformer I. Our ATCA results have ruled out the detection of glycine ( both conformers I and II) in the compact hot core of the LMH at the levels reported, so we conclude that it is unlikely that Kuan et al. have detected glycine in either Sgr B2 or Orion-KL. We find upper limits for propylene oxide abundance of 3.0 x 10(14) cm(-2) in Orion-KL and 6.7 x 10(14) cm(-2) in Sgr B2 (LMH). We have detected fourteen features in Sgr B2 and four features in Orion-KL which have not previously been reported in the interstellar medium, but have not been able to plausibly assign these transitions to any carrier.