Odds may still favor the eventual construction of former President Barack Obama’s $500 million museum and library in a public park along Chicago’s lakeshore, but it’s no longer a sure thing in the face of a formidable legal challenge by a parks advocacy group.

U.S. District Judge John Robert Blakey is hearing arguments Thursday in Chicago on a key motion by city attorneys to toss a lawsuit by Protect Our Parks that aims to halt the Obama Presidential Center from ever being built in the selected location.