They say the requirement is discriminatory and violates their constitutional rights.
The three oppose the oath on religious or conscientious grounds, saying pledging allegiance to Canada should be enough.
They also note that those who are citizens because they were born in Canada don't need to take any oaths.
For its part, the federal government argues the oath to the Queen has been around since Confederation.
It also says the three are in Canada voluntarily and are free to follow their political or religious dictates as permanent residents — and that not having the benefits of citizenship is a reasonable cost of their personal beliefs.