We have used the Australia Telescope Compact Array (ATCA) to conduct a search for the simplest amino acid, glycine (conformers I and II), and the simple chiral molecule propylene oxide at 3 mm in the Sgr B2 LMH. We searched 15 portions of spectrum between 85 and 91 GHz, each of 64 MHz bandwidth, and detected 58 emission features and 21 absorption features, giving a line density of 75 emission lines and 25 absorption lines per GHz stronger than the 5σ level of 110 mJy. Of these, 19 are transitions previously detected in the interstellar medium (ISM), and we have made tentative assignments of a further 23 features to molecular transitions. However, as many of these involve molecules not previously detected in the ISM, these assignments cannot be regarded with confidence. Given the median line width of 6.5 km s−1 in Sgr B2 LMH, we find that the spectra have reached a level where there is line confusion, with about 1/5 of the band being covered with lines. Although we did not confidently detect either glycine or propylene oxide, we can set 3σ upper limits for most transitions searched. We also show that if glycine is present in the Sgr B2 LMH at the level of N= 4 × 1014 cm−2 found by Kuan et al. in their reported detection of glycine, it should have been easily detected with the ATCA synthesized beam size of 17.0 × 3.4 arcsec2, if it were confined to the scale of the LMH continuum source (<5 arcsec). This thus puts a strong upper limit on any small-scale glycine emission in Sgr B2, for both of conformers I and II.