Kevin Costner in Court I Did NOT Defraud A Baldwin

6/4/2012 9:42 AM PDT

Kevin Costner In Court -- I Didn't Defraud a Baldwin Over BP Oil Disaster

Breaking News

Kevin Costner
is ready to prove to a jury he's not a fraud ... despite what Stephen Baldwin says -- because the courtroom showdown starts today in New Orleans.

TMZ broke the story ... Baldwin sued Costner back in 2010, claiming the actor duped Baldwin into selling shares in a company that builds machines designed to clean up oil spills.

Baldwin claims Costner and his business partner knew that the company was about to score a bonanza by selling the machines to help clean up the BP disaster, but withheld the info from Baldwin, who then sold his shares back to the company, not knowing about the looming windfall.

Costner claims there was no firm deal to sell the machines to BP when Baldwin dumped his shares ... adding he had no idea that Baldwin was even interested in selling.

Costner's company scored a $52 million deal with BP, and Baldwin now wants $21 mil for his troubles.

Jury selection has just gotten underway. Thanks to WGNO for the video.