I am ordering a copy of my birth certificate online at vitalchek and it requires the fathers first and last name. My problem is I don't know who my father is and neither does my mom. What do I need to put their? Has anyone else had this problem?

It wants the fathers name as listed on the birth certificate.
If there was none or if it was marked unknown when the birth certificate was issued.

If the online form will not allow you to leave it blank, you need to contact their tech support as to options.

To make it easier on you, just call up the County where the birth certificate was issued and ask them for the procedure to obtain yours. It's cheaper and easier in the end to go directly to the state versus the vitalcheck route. They charge an arm and a leg for the Fedex shipping as well or you have to wait for 4 weeks for the state to process the request through them anyway. I had to wait almost 4 weeks and I went through vitalcheck but did not opt for the pricey Fedex delivery. I would have been ahead of the game going directly to the state. You can also check online at your particular state to see if they have a downloadable form to use (mine did).