First, meet with each individual separately. Speak to them in general terms, like you know something is between them, but that it is having a negative impact on the business, so it is now your concern, as manager.
Ask them if they understand how the issues between them can effect the rest of the department, and if either of them do not understand, then calmly explain it to them.
Then, ask each of them, if, for the good of the department / company, would they be willing to put this issue to bed, if the other party would agree to, as well. You are asking for a professional commitment from each of them, and it is concerning a business issue, so this is in line with your job as manager.
If the first person agrees to this, then go to the second person, and tell him/her that the other person has agreed to put their issue to bed, so would he/she also agree to do so? If the answer is yes, then you bring them both together, and say that each of you has made a commitment to me, your boss, to put this issue between you behind you. I appreciate your efforts in doing so, and while I have no expectations that you will become close friends, I do expect you to be civil to one another, as we are all on the same team here.
If one or the other person can not make the commitment to put the issue to bed, then that person needs to be advised to look elsewhere for work, since they are a disruptive force in the department.
If neither party will commit to putting the issue to bed, then you have some choices to make. You can decide which one is more valuable to your team, and let the other go, OR, you can decide that both of them are disruptive to the teamwork that you require, and let them both go, telling them that they have brought this on themselves by their inability and refusal to get along civilly.
Doing nothing in NOT an option! As manager, your team depends on you to keep the ship running smoothly. This is not an issue between 2 people - it is a team issue, and all eyes are on you to see how you reslove it.