From my understanding of light, you are always looking into the past based on how much time it takes the light to reach you from what you are observing.

For example when you see a star burn out, if the star was 5 light years away then the star actually burnt out 5 years ago.

So I am 27 years old, if I was 27 light years away from Earth and had a telescope strong enough to view Earth, could I theoretically view myself being born?

Yes, you can.  And you do not even need to leave the Earth to do it.  

You are always viewing things in the past, just as you are always hearing things in the past.  If you see someone do something, who is 30 meters away, you are seeing what happened $(30\;\mathrm{m})/(3\times10^8\;\mathrm{m}/\mathrm{s}) = 0.1\;\mu\mathrm{s}$
in the past.  

If you had a mirror on the moon (about 238K miles away), you could see about 2.5 seconds into earth's past.  If that mirror was on Pluto, you could see about 13.4 hours into Earth's past.

If you are relying on hearing, you hear an event at 30 m away about 0.1 s after it occurs.  That is why runners often watch the starting pistol at an event, because they can see a more recent picture of the past than they can hear.

To more directly answer the intent of your question:  Yes, if you could magically be transported 27 lightyears away, or had a mirror strategically placed 13.5 lightyears away, you could see yourself being born.
