The Conseil des Innus de Ekuanitshit oppose a plan by Newfoundland and Labrador Hydro, now Nalcor Energy, to build two power plants on the Churchill River.
The project was approved after a provincial and a federal environmental assessment by a joint review panel, which also recommended a series of mitigation measures.
The panel said the impact on Quebec aboriginal land and resource uses after the mitigation efforts would be adverse, but not significant and that the benefits would outweigh the environmental and economic impacts.
The federal cabinet approved the project in 2012, again stipulating certain environmental mitigation measures, and the Innu sued, losing at both the Federal Court and the Federal Court of Appeal.
As usual, the Supreme Court gave no reasons for refusing to hear the case.