Question: I am living in the United States out of status as of the moment. I have never been deported, never had a brush with the law and pay my taxes on time. Do I have a chance of moving permanently to Canada?
Answer: If you are thinking of applying for Canadian immigration, your being out of status in the US or any other country will generally not affect your application. However, it may reduce your eligibility when you apply through the Quebec provincial nominee program, where only work experience accrued while an applicant is in status will be counted.
If you are actually planning to apply for a temporary resident visa (visitor or tourist visa), you could be wasting your time. As it is, applications for temporary residence lodged by individuals who are already overstaying in another country will be automatically refused for obvious reasons.