The drawing below is a hyper simplification of what atheist scientists would like you to believe.  The truth is that the title is a misrepresentation and untrue.  DNA does not replicate itself.   Below the drawing is an actual, though still simplified explanation of the truth about DNA replication.

DNA does not replicate itself.  Proteins are needed for DNA Replication.  Proteins, however, are made using information existing in DNA.   In other words, DNA is needed to make the proteins which make DNA.  This may be the ultimate chicken and egg paradox.  Which came first and how was either made without the other? 

The reality is that to be replicated, DNA requires the existence of and coordination of all the molecules and proteins listed at the bottom of this page.  The proteins are complex molecules made from the information contained in the DNA and the proteins are made via even more complex processes involving multiple molecular machines!

To make matters worst (for materialistic science) DNA resides in the nucleus as a ball of string like molecules. For DNA replication to occur, all the following proteins aid in the unwinding and separation of the DNA molecule still in its double stranded form. These proteins are required since DNA is a very stable molecule and cannot be replicated unless it is first separated into two single-stranded parts.

Compare the list below with the diagram and you will see that DNA does not replicate itself as those who try to have you believe that life is simple and it origins easily explained by science.  

The proteins needed and which must work together to cause DNA replication are:

1. DNA Helicases which are proteins that bind to the double stranded DNA and act to separate two strands.
2. DNA binding proteins which bind to the DNA and act speed up the process by about 100 times.
3. DNA binding proteins for the single strands which increases the rate replication by about 100 times.
4. DNA Polymerase another enzyme.
5. DNA Gyrase another enzyme.
6. Ligase which is required to repair errors in the replication.

Each of these proteins represents a chicken and egg paradox for simplistic reductionistic/materialistic science.

Click here for a site with a more detailed description.

Unraveling DNA's Design  (Yes a Christian site with one of the best description of DNA replication.)