In 2011, Thater received an Award for Artistic Innovation from the Center for Cultural Innovation in Los Angeles. She used the grant to complete "Chernobyl", a large-scale installation project which documents the post-human landscape at the Chernobyl nuclear power plant site in the Ukraine, marking the 25th anniversary of the explosion in 2011. She has been the recipient of other notable awards, including the Phelan Award in Film and Video (2006), a John Simon Guggenheim Memorial Foundation Fellowship (2005), an Étant-donnés Foundation Grant (1996), and a National Endowment for the Arts Fellowship (1993).