Things are heating up between Tesla and Chrysler.

In what has evolved from a slight jab to a full-on brawl, Tesla CEO Elon Musk fired back at Chrysler on Thursday after the Auburn Hills-based automaker claimed that it was actually the first American car maker, not Tesla, to fully repay government loans.

As a quick backdrop, the war of words between Tesla and Chrysler began Wednesday night after Tesla fully paid off its government loans. In a press statement announcing the repayment, Tesla stated that it was the "only American car company to have fully repaid the government," prompting Chrysler to counter on its corporate blog that it actually repaid its government loans two years ago.

While Chrysler is correct in saying that it paid off its government loans in 2011, there are enough loopholes in that statement - as pointed out on these pages - for Tesla to claim that it is, in fact, the first American car company to fully pay back Uncle Sam. Musk highlighted some of those technicalities on his Twitter account on Thursday.

"As many have already noted, Chrysler is a division of Fiat, an Italian company. We specifically said first 'U.S.' company," Musk wrote on Twitter. "More importantly, Chrysler failed to pay back $1.3B. Apart (from) those 2 points, you were totally 1st."

The U.S. government received $11.2 billion of the $12.5 billion it loaned Chrysler, but it stated in July of 2011 that it didn't expect to recover that $1.3 billion shortfall. Technically, that was all Chrysler had to do to satisfy the government's loan requirements.

Chrysler spokesman Gualberto Ranieri, who wrote the blog post for the automaker, called the entire situation "pretty ridiculous."

"I am the first to understand that this is open to an endless debate," Ranieri told The Detroit News. "Technically, Chrysler was the first to repay its government loans, General Motors was the second."