My ex-spouse took property that was to go to me in my Harris County divorce. Can he or she discharge the debt in chapter 7 bankruptcy?

Not if you fight it.

The 5th Circuit Court of Appeals recently decided that if an ex-spouse takes property that was awarded to the other spouse in a divorce, the resulting debt may not be discharged in a chapter 7 bankruptcy because it is a "willful and malicious injury" under the Bankruptcy Code Section 523(a)(6). In the Matter of Shankle, Court of Appeals, 5th Circuit 2014.

But keep in mind that this is only in chapter 7. If the debtor (the person that filed bankruptcy) files chapter 13 instead, then the debt may be discharged, so long as the debtor completes the plan.

And don't forget that even if it is a willful and malicious injury in a chapter 7 case, to keep the debt from being discharged you must file an "adversary proceeding" or lawsuit in Bankruptcy Court to challenge the discharge of the debt, and there are strict time limits. Currently, you must file your complaint within 60 days after the first date set for the Meeting of Creditors, or it is too late. See Bankruptcy Rule 4007(c).

You will almost certainly also need a lawyer to file an adversary proceeding. Only you can decide if it is worth it to you to do it. And keep in mind that even if you win, that doesn't mean your ex-spouse will actually pay you. A civil judgment, even a non-dischargeable one, is not enforceable by contempt. In other words, if they don't have the money you may just be out of luck anyway.