US President George Bush has nominated John Roberts to succeed Chief Justice William Rehnquist who died on Saturday.
Not one senator has shown outright opposition to Judge Roberts
Mr Roberts had originally been nominated to replace another Supreme Court judge who is retiring, and was awaiting Senate confirmation.
Mr Bush described him as a man of integrity and fairness with a reputation for goodwill and decency.
Democrats will want to question him on issues such as abortion, church-state matters and the environment.
However correspondents say his nomination is unlikely to prove controversial.
Mr Rehnquist, a conservative appointed chief justice by President Reagan in 1986, died at the age of 80 on Saturday from thyroid cancer.
Mr Roberts, 50, said he would be honoured "to succeed a man I deeply respect and admire".
Born in Buffalo, raised in Indiana
Graduated from Harvard in 1979
Was clerk to Chief Justice Rehnquist and then served in the Reagan administration
Serves on the District of Columbia appeals court
Has argued before the Supreme Court 39 times
President Bush will now have to nominate another person to fill the vacancy left by Justice Sandra Day O'Connor, who announced her retirement in July. He said he would do so in a "timely manner".
Ms O'Connor has offered to continue her duties until a successor is found.
Mr Bush said he hoped the Senate would confirm Mr Roberts' appointment within a month, when the Supreme Court is due to reconvene.
Hearings had been due to start on Tuesday afternoon, but it now seems likely they will not begin until Thursday, after Mr Rehnquist's funeral.
If Judge Roberts is not confirmed before the court resumes work in October, Mr Rehnquist's administrative duties will be taken over by liberal Justice John Paul Stevens until a new chief is confirmed.
Judge Roberts serves on the US Court of Appeals for the District of Columbia.
He graduated from Harvard Law School with flying colours in 1979, and was a former clerk to Chief Justice Rehnquist before serving in the Reagan administration.
He has argued before the Supreme Court 39 times as a private or government lawyer.