An optimistic Chrysler narrowed its net loss significantly in the fourth quarter and it forecast a net profit for 2011 as it continued a comeback from bankruptcy protection.

Chrysler, which is controlled by Italy’s Fiat Group SpA, today predicted it would make $200 million to $500 million this year, setting the stage for an initial public stock offering that could take place in the fourth quarter.

The U.S. government gave Chrysler $12.5 billion to get through bankruptcy in 2009. In exchange, the government got a 10 percent stake in the company. Chrysler still must repay $5.8 billion on the loans, and the government hopes to get the rest of its money back in the stock sale.

Chrysler, which has not turned a quarterly profit since leaving bankruptcy, said this morning that it lost $199 million from October through December, far better than the $2.7 billion it lost during the same period of 2009.

For the full year in 2010, Chrysler lost $652 million, compared with a staggering $8 billion loss in 2009 when it would have run out of cash without government help.