During the 1980s, several Americans were captured in Lebanon amidst the civil war there. Some of the Americans, including the CIA station chief at the time, were captured by Hezbollah, an Iranian backed militia. To bring these hostages home, members of the Reagan administration secretly negotiated with Iran to sell arms to the Iranians (who were at war with Iraq) for help in getting the hostages released. (As an aside, the monies from this sale was diverted to the Contras, a Nicaraguan rebel group against the pro-Soviet Sandinista regime. a.k.a. the Iran Contra-Affair)
This is a great question. The short answer is: Despite the common rhetorical mantra from American politicians that "the United States does not negotiate with terrorists," in practice the country regularly negotiates with terrorist groups.
First, let's talk about the different kinds of terrorist groups. There are separatist groups like the ETA, the PLO and the IRA who all used terroristic tactics in order to pursue their goals of securing independence or greater autonomy/sovereignty from their host country. Then there are more fanatical groups driven by nihilistic ideologies, such as al Qaeda or Aum Shinrikyo. The former groups want(ed) something tangible like land or independence, whereas the latter groups want(ed) something that is more intangible, like the complete destruction of Western culture.
Suffice to say, the United States is much more willing to negotiate with groups who want something tangible. Though the US designated the PLO as a terrorist group until 1991, we always found ourselves at the negotiating table with both the PLO and the Israelis on a regular basis throughout the cold war.
Of course, this gets tricky, because it's difficult to say the US negotiates with terrorist groups when not everyone agrees on what a terrorist group is or isn't. Obviously, the US was in the minority in designating the PLO as a terrorist group.
Since this is /r/AskHistorians, I won't get into how we have negotiated with terrorist groups in recent history. But if we are to consider the 1960s-80s era PLO as a "terrorist" group, as the US government did, then yes: we regularly negotiated/mediated with them in regard to the Israel-Palestine dispute.
Source:
Neumann, Peter. Negotiating With Terrorists. Foreign Affairs. 2007.