The 17-year-old German student named only as Diren entered Markus Kaarma's garage in April after the former fireman left it open.
After Diren tripped motion sensors placed at the entrance of the garage, Kaarma and his girlfriend observed a male figure moving around on video monitors from cameras inside.
Kaarma rushed outside and fired four shots with a shotgun into the darkness, hitting the student twice and killing him.
“He knowingly and purposefully caused Diren's death,” prosecutor Andrew Paul said. “That is the exact definition of murder.”
Diren's father and other family members were present in the courtroom to hear the beginning of the hearings, wearing T-shirts printed with the words “You will always be in our hearts”.
Court documents show that Kaarma claims to have acted in the heat of the moment after hearing “metal on metal” and assuming the intruder would attack with a knife or tool.
But his girlfriend Janelle Pflager said she heard Diren say “wait” before Kaarma opened fire.
Prosecutors say that the homeowner left the garage open as a trap for potential thieves after his house was broken into twice in three weeks.
A detective reported a call from a neighbour saying that Kaarma had told her “I'm just waiting to shoot some f*cking kid” when she asked how he was doing.
But Kaarma says that he believed he and his family were in danger and that he shot in self-defence.
Montana law includes strong legal support for the right of self-defence in one's own home under the so-called “Castle Doctrine”.
And more than 57 percent of people in Montana own at least one firearm, putting it third on the list of most-armed US states behind Wyoming and Alaska.
The fact that Diren entered the garage is not under dispute, but the court must now decide whether Kaarma was really in fear for his own life and that of his family or whether he had planned to kill.
It has been confirmed that Diren was not the original thief who stole cash, a mobile phone and other items from the garage, although he was entering it illegally.
Kaarma has been released against a relatively low bail of $30,000 (€24,000).