Ugandan opposition leader Robert Kyagulanyi, popularly known as Bobi Wine, wants the chief justice to recuse himself from hearing a petition challenging the re-election of President Yoweri Museveni.
Bobi Wine accuses Justice Alfonse Owiny-Dollo of bias because of his close association to the president.
The opposition politician also wants two other supreme court judges to recuse themselves from the petition on similar grounds.
The three judges have not responded to the accusations.
Chief Justice Owiny-Dollo was President Museveni’s lawyer in 2006, according to the Nile Post website.
Justice Mike Chibita was Mr Museveni’s private secretary on legal affairs, while Justice Ezekiel Muhanguzi is a relative of Security Minister Elly Tumwine, according to local media.
Bobi Wine argues that the three cannot hear the petition without bias.
President Museveni won a sixth elected term last month. Bobi Wine, his main rival, said the election was rigged, but Mr Museveni said it was the fairest vote ever.