This is a great question. I would say that there are three important traits that a contract negotiator needs to possess. First, a contract negotiator needs to know the field that he or she is in very well. Negotiators needs to know what others are making, which companies are charging what, and other information that surrounds these topics.
Second, negotiators need to have great people skills. They need to satisfy two parties that are not necessarily friendly towards each other. Hence, sensitivity and tact are essential.
Finally, a negotiator needs to have a reputation of fairness and more importantly, he or she actually needs to be fair. This last quality cannot be overemphasized. Both parties need to know that they are getting a fair deal.