First Look at Derek Chauvin Behind Bars Since 22.5 Year Sentence

Here's the first look at Derek Chauvin behind bars since he was sentenced for murdering George Floyd, and he looks ... well, sleepy with a measure of defiance.

TMZ's obtained Chauvin's first mug shot in prison ... a place he'll call home as he serves his 22.5-year sentence. He kept a stiff upper lip as he mugged for the camera in his orange standard issue. He also looks like he's struggling to keep his eyes open ... he looks out of it.

We're told the Minnesota Department of Corrections snapped the new mug shot June 28 ... just 5 days after his sentencing.

As you know ... Chauvin was found guilty of 2nd-degree unintentional murder, 3rd-degree murder and 2nd-degree manslaughter ... but the 2nd-degree conviction is what sticks.