They argue the requirement is discriminatory and violates their constitutional rights and should be struck down.
The three oppose the oath on religious or conscientious grounds, saying it should be optional or that pledging allegiance to Canada should be enough.
A lower court judge, however, disagreed, saying any charter violation can be justified in a democratic society.
One of the three, Michael McAteer, said Canada is supposed to be an inclusive country and he feels the oath is not necessary.
"I'm a democrat," said McAteer, who is from Ireland. "I believe in democracy, equality, and I think any monarchy is the very antithesis of a democratic society."
"I want to become a citizen without taking an oath to what I consider to be a foreign queen," he said, adding people who are born Canadian don't have to take an oath.
Ottawa argues the oath has been around for ages, nothing forces permanent residents to become citizens, and nothing precludes them from opposing the monarchy.
The government has already made it clear it will take the case to the Supreme Court of Canada if it loses before the Ontario Court of Appeal.