measured with STM/S*

We used scanning tunneling microscopy and spectroscopy to investigate the local symmetries of the electronic states in FeSe_1-xS_x. In tetragonal samples with x=0.23 , where nematic order is absent, our spectroscopic mapping experiments reveal a myriad of quasiparticle interference wave vectors in the -60 to 25 meV region, all of which are accurately captured by our and ARPES-calibrated theoretical simulations. The experiments also demonstrate the existence of a periodic pattern for states near the Fermi level that breaks both translational and rotational symmetry. These patterns are non-dispersive and are not seen in the theoretical calculations. Phenomenologically, this broken-symmetry state reminds us of the charge order in the cuprates, suggesting that strong electron correlations might be involved in its formation.