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The justices will weigh if Colorado can strike Mr Trump off its ballot after finding he engaged in insurrection over the US Capitol riot.
Their decision will also determine if similar bids to keep Mr Trump off the ballot in other states are valid.
He is the definitive frontrunner to be the Republican party’s candidate.
Unless the justices rule against Mr Trump, he looks likely to challenge Democratic President Joe Biden in November.
It is the most consequential such case to reach the court since it halted the Florida vote recount in 2000, handing the White House to Republican George W Bush over Democrat Al Gore.
The challenge has been expedited by the US Supreme Court, and there is pressure for a decision before 5 March, when voters in 15 states – including Colorado – cast their ballots in Republican primaries.
Mr Trump’s name so far remains on the Colorado ballot, pending the court’s ruling. Maine also has excluded Mr Trump from its ballot, a decision on hold, too, while the justices consider the matter.
The legal challenge hinges on a Civil War-era constitutional amendment that bans anyone who has “engaged in insurrection or rebellion” from holding federal office.
This prohibition has never been used to disqualify a candidate for president.
In December’s ruling, the Colorado Supreme Court wrote that it was aware of the magnitude of its decision.
“We are likewise mindful of our solemn duty to apply the law, without fear or favor, and without being swayed by public reaction to the decisions that the law mandates we reach,” the justices wrote.
In turn, Mr Trump’s lawyers argued that the Colorado ruling had “unconstitutionally disenfranchised millions of voters in Colorado” and could be used to further disenfranchise millions more across the country.
His argument has been supported by the chief legal officers of 27 states, who filed a brief saying the Colorado ruling would sow “widespread chaos”.
“Most obviously, it casts confusion into an election cycle that is just weeks away,” the attorneys general wrote. “Beyond that, it upsets the respective roles of the Congress, the States, and the courts.”
Courts in Minnesota and Michigan have dismissed parallel efforts to remove Mr Trump from their ballots, while other cases, including in Oregon, are pending.
Continue here: BBC
