The historic treaty, which forced the Cherokee people off their ancestral lands across the Southeast and onto the infamous Trail of Tears in 1835, was supposed to give them official representation in Washington in exchange.
It has never happened.
"The promise was very simple," said Cherokee Principal Chief Chuck Hoskin, Jr. "The treaty literally says the Cherokee Nation 'shall have' a right to a delegate in the House of Representatives."
The non-voting position, similar to a role held by representatives of the District of Columbia, Guam, American Samoa and the U.S. Virgin Islands, would give the Cherokee a voice at the epicenter of political power.
Delegates are able to sit on committees, introduce bills, and give speeches on the House floor, even if they cannot participate in an up-or-down vote on final legislation.
There are currently six non-voting delegates in the U.S. House. No Native American tribe has ever been formally represented.
"Thinking about the fact that the U.S. has held the Cherokee Nation accountable for treaty obligations, we now see an opportunity to get some justice by asserting this right," Hoskin said.
For generations, the promised position was overlooked and unfilled. But in 2019, the tribe named Kim Teehee - a former Obama administration advisor - to be its delegate, and Hoskin began a campaign to get her seated.
"There has been a need to educate members of Congress," Hoskin said. "I think the only thing that has stood in our way really is this learning curve."
The Treaty of New Echota, negotiated with the administration of President Andrew Jackson and ratified by the Senate, set into motion a mass migration from what is now parts of Georgia, Alabama, North Carolina and Tennessee to make way for white settlers.
16,000 Cherokee trekked west to Oklahoma. A quarter of them -- 4,000 people -- died along the way.
"To seat the delegate would give some small measure of justice to those who lost their lives" on the Trail of Tears, Teehee said on Capitol Hill this month after a House Rules Committee hearing on the issue. "I feel like I'm in a full circle moment here, because I'm representing the treaty right that they died for," she said.
Seating a Cherokee delegate -- and fulfilling the government's promise -- has rare bipartisan support in the House.
"I'm glad to see tribes advocating for their treaties with such conviction," said Rep. Tom Cole, R-Oklah., the top Republican on the House Rules Committee, who is Native American.
"If it were up to me, you know, I would seat a delegate team tomorrow," said Committee Chairman Rep. Jim McGovern, D-Mass. "But obviously there are some issues that need to be resolved."
There is little organized or outspoken opposition to seating a Cherokee delegate, but lingering legal and procedural questions have complicated the tribe's campaign.
One sticking point: the potential perception that Cherokee Americans could effectively get a "super vote" in Congress -- represented by their delegate and the congressperson from their district. (As American citizens, Cherokee members can vote in federal elections.)
"It's uncomfortable for non-Indians to think about the possibility of Cherokees having an extra say, but it was also uncomfortable for the Cherokees to be forced out of Georgia,' said Ezra Rosser, a law professor and specialist in Indian Law at American University Washington College of Law.
"Are we as a society ready to take seriously the obligations that we owe to tribes?" Rosser asked. "That has legal components around it, but it's largely about what we as a country believe in."
There is also the question of whether creation of a new seat in the House needs a new vote from both chambers of Congress and a signature by the president.
"Then, there's the courts," added Rosser, "which I think without question would be asked to weigh in on this."
Teehee notes that the Treaty of New Echota was ratified by the Senate and signed by the president 187 years ago. "It is already the supreme law of the land," she said.
"And that's why we've had nearly unanimous support throughout the country from other Indian tribes expressing support for us," she said. "But in addition to that, it'll be an opportunity for us to continue to educate my fellow colleagues about the issues that pertain to us."
Chief Hoskin says he is optimistic the Cherokee Nation is on the verge of making history in the 118th Congress, which begins in January 2023. But he concedes progress on Capitol Hill is notoriously unpredictable and painfully slow.
"If you're a tribal leader, and you know your history, you understand the value of patience," Hoskin said. "I also understand that we're talking about the Congress of the United States, an institution in which Cherokees have often not only struck out but have been on the receiving end of a great deal of injury."
In a statement, outgoing House Speaker Nancy Pelosi said the Cherokee are "entitled" to representation and that Democrats "will continue to explore a path" forward.
Republican leader and leading GOP candidate for House Speaker Kevin McCarthy did not respond to ABC News' requests for comment on the seating of a Cherokee delegate.
" I think most Americans, if they think about what makes the country great, being a country that keeps its word is one of those thoughts – and this is a great opportunity for the country to keep its word," Hoskin said.