The Ross River Dena Council is asking the Yukon Supreme Court to force the federal government back to the negotiating table.
The First Nation and the federal government have been stalled for years in discussing a land claim.
Eleven of Yukon's 14 First Nations currently have such agreements, which set boundaries and give them political and legal authority over land as well as the right to 'draw down' responsibilities for self-government.
Attorney Stephen Walsh, representing the Ross River Dena Council, says the federal government made a "take it or leave it" offer in 2002.
"There is an unfortunate lack of willingness on the part of Canada to resume negotiations in the 15 years since negotiations ended," Walsh told the court this week.
The First Nation's long and complex process of discussing self-government began in 1973.
Offer 'pennies per acre of traditional land'
One issue that has continually separated the two sides is compensation.
The federal government provides money to First Nations who sign land claims, as the allocated settlement lands are most often smaller than First Nations' traditionally-claimed land.
In the case of the Ross River Dena Council, the federal offer for financial compensation under the terms of Yukon's Umbrella Final Agreement would be $14,347,330, adjusted for inflation from 1989.
Walsh told the court this was not "generous" and said it accounts to a "net surrender" of traditional land for what he claimed to be less than 50 cents an acre.
The Ross River Dena Council is part of the Kaska Dena Council, a group of five different Kaska First Nations.
Walsh described the Yukon area as 27 million acres, or more than 100,000 square kilometres.
Umbrella Final Agreement not legal, argues lawyer
The federal government has said it must abide by the terms of the Umbrella Final Agreement, which sets rates for compensation.
The document also sets boundaries between different First Nations and their often-overlapping claims to land.
One controversial part of the case is that the Ross River Dena Council argue Yukon's Umbrella Final Agreement is not a valid legal document. Their argument is procedural as they argue it was never properly signed.
Yukon Supreme Court Justice Leigh Gower is hearing the case — being asked to determine if the federal government has met its constitutional obligations towards the Ross River Dena Council, and whether it has proceeded with honour, he said.
"I'm trying to determine if the negotiations were in good faith," he said.