Can employer sue me for quitting?

I am in talks with a consulting firm in the United States with regards to a position they got in touch with me for. According to them they will be training me for a position that their clients require. I have the necessary education its just that the job requires a little familiarity with the role and responsibility. For which they would provide training. They have mentioned in their contract that I will be required to pay them $25000 if I quit prior to 12 months of starting the project at their client. My question is are they actually allowed to ask for this 25000 dollars in compensation given the fact a few months down the line I secure a better job or a more interesting opportunity and want to quit.