An employer does have the right to sue for breach of an employment contract. Whether the contract at issue here is enforceable will depend on the terms of the contract, and possibly the facts surrounding the formation of the contract, and events transpiring thereafter. If the contract is enforceable, the damages, if any, to which the employer would be entitled might be reduced given that the employer eventually hired another employee three months later, but again, that would depend on the facts and circumstances of the case and more importantly, on the language in the contract. If the employer is suing, you really need to retain an employment attorney in the jurisdiction where the suit is pending. Although I have no idea as to what is in the contract, you could be looking at paying damages plus the employer's attorney's fees - which, if the case drags on, could add up to being be tens of thousands of dollars. Any reasonable expense you incur in hiring a good attorney will probably be money well spent. I have seen employees try to "go it alone" without an attorney in cases of this type, and I have never seen it come out well for the employee.
The terms of the agreement are important and will likely determine your employer's success. You need to find an attorney to review this situation in private as soon as possible.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.