CHICAGO (AP) — Odds still favor the eventual construction of Barack Obama’s $500 million presidential 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.

A federal judge in Chicago hears arguments Thursday on a city motion to toss the group’s lawsuit that argues the project runs afoul of laws barring development in parks hugging Lake Michigan.

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A ruling for Protect Our Parks could signal the Obama Presidential Center is in real trouble.

Recent Chicago history illustrates such suits can kill blockbuster projects, even ones proposed by VIPs with enormous influence.

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Three years ago, a lawsuit brought by Friends of the Park helped scuttle a $400 million plan by “Star Wars” creator George Lucas for a museum on Chicago’s lakefront. It’s now under construction in Los Angeles.

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