The art and science of negotiation is undergoing its biggest transformation in decades.Our research, involving 120 experienced negotiators in complex business deal simulations, demonstrates that LLMs fundamentally change negotiation dynamics.When only one party has access to LLM support, they achieve notably better outcomes: buyers gained 48.2% and sellers 40.6% more value compared to their counterparts.Even more compelling, when both parties use LLM support effectively, joint gains increase by 84.4% compared to traditional negotiations.However, achieving these results requires mastering both negotiation fundamentals and LLM capabilities. Neither alone is sufficient.