Not Chapter 7, which would involve a liquidation, but Chapter 11, which would involve a recapitalization, etc., with the expectation that a New Kodak would emerge that is financially viable. (This process is one that the President did not allow GM to undergo.) The federal bankruptcy judge, however, can find that there is no financially viable Kodak appropriate for Chapter 11 and can move it into Chapter 7 (as a judge could have done with a GM bankruptcy).
The company has a huge pension burden. According to the WSJ's blog, the company spent $245 million on pensions and other benefits for retirees in 2011 when it generated only $93 million:
Kodak says it has “been unable to reduce the amount of cash consumed by post-employment benefit obligations to make them proportional to a financially smaller Kodak.”
The "pension and other benefits" matter can be dealt with in Chapter 11 and in Chapter 7. The US Treasury will be on the hook for at least some of those benefits in either case.