Here is another option for modern browsers:
.child {
  position: absolute;
  left: 50%;
  top: 50%;
  -webkit-transform: translate(-50%, -50%);
  -moz-transform: translate(-50%, -50%);
  -ms-transform: translate(-50%, -50%);
  -o-transform: translate(-50%, -50%); 
     transform: translate(-50%, -50%);
}