We present initial results from the Cosmic Ultraviolet Baryon Survey ( CUBS ) . CUBS is designed to map diffuse baryonic structures at redshift z\ > ^ { < } _ { \sim } \ > 1 using absorption-line spectroscopy of 15 UV-bright QSOs with matching deep galaxy survey data . CUBS QSOs are selected based on their NUV brightness to avoid biases against the presence of intervening Lyman Limit Systems ( LLSs ) at z _ { abs } < 1 . We report five new LLSs of \log N ( { \mbox { H { \scriptsize I } } } ) / \mbox { $ { cm ^ { -2 } } $ } \ > ^ { > } _ { \sim } \ > 17.2 over a total redshift survey pathlength of \Delta z _ { LL } = 9.3 , and a number density of n ( z ) = 0.43 _ { -0.18 } ^ { +0.26 } . Considering all absorbers with \log N ( { \mbox { H { \scriptsize I } } } ) / \mbox { $ { cm ^ { -2 } } $ } > 16.5 leads to n ( z ) = 1.08 _ { -0.25 } ^ { +0.31 } at z _ { abs } < 1 . All LLSs exhibit a multi-component structure and associated heavy ions from multiple ionization states such as C II , C III , Mg II , Si II , Si III , O VI absorption . Differential chemical enrichment levels as well as ionization states are directly observed across individual components in three LLSs . We present deep galaxy survey data obtained using the VLT-MUSE integral field spectrograph and the Magellan Telescopes , reaching sensitivities necessary for detecting galaxies fainter than 0.1 L _ { * } at d\ > ^ { < } _ { \sim } \ > 300 physical kpc ( pkpc ) in all five fields . A diverse range of galaxy properties are seen around these LLSs , from a low-mass dwarf galaxy pair , a co-rotating gaseous halo/disk , a star-forming galaxy , a massive quiescent galaxy , to a galaxy group . The closest galaxies have projected distances ranging from d = 15 to 72 pkpc and intrinsic luminosities from \approx 0.01 L _ { * } to \approx 3 L _ { * } . Our study shows that LLSs originate in a variety of galaxy environments and trace gaseous structures with a broad range of metallicities .