Choose Random Cell From Range Value Unless Equals 0

So the range I am trying to attain cell values from looks like this

      A
1   John
2   
3   Michael
4   Edward
5
6   George
7
etc.

This is the formula I'm using:

=INDEX($A:$A,RANDBETWEEN(1,COUNTA($A:$A)),1)

My only problem is that if it finds a cell with no value in it the value it returns is "0". Is there a way for it to reject values that equal "0" and have it choose another random cell?

Thanks in advance.