Muthiora Kariara, a political novice who is running with independent presidential candidate Japheth Kaluyu, answered questions for about an hour.
Some of the candidates were not allowed to take part because they arrived late.
Political parties have accused the organisers of failing to consult them in the planning of the event.
The main candidates for deputy president, the current holder of the office William Ruto and Kalonzo Musyoka of the opposition National Super Alliance, boycotted the debate.
Viewers who tuned in saw a stage set with six podiums at the Catholic University of East Africa in Nairobi - but only one of them occupied.
BBC Africa reporter James Copnall says Muthiora Kariara did not look overawed, even when the moderators appeared to struggle to pronounce his name.
He took part in what became a solo question and answer session broadcast live to the nation - perhaps the best political advertising a newcomer could wish for, our correspondent adds.
A TV debate for Kenyan politicians hoping to become deputy president in next month's elections went ahead even though only one candidate took part.