OK 'abiogenesis' is the biggie in Chemistry and Biology - not my exact field but here's some pointers.
A lot of interest was first sparked (excuse the pun) by the Miller-Urey experiment back in the 50s which took a lot of the chemicals about in the early earth, heated them and passed a spark through for several days and found traces of most of the amino acids necessary for life
We're not going to be looking for DNA - that's way to complex and a RNA basis may even be too complex althougth the 'RNA world' hypothesis suggests this others suggest a 'Thioester world' where sulphur chemistry is the key role
http://en.wikipedia.org/wiki/Miller%E2%80%93Urey_experiment
Amino acids are the building blocks of proteins which in turn are the building blocks of life.
But that's not the same as a self replicating chemical - by a long shot.
The cell membrane is another important early requirement as you need a structure to keep everything together and an energy capture mecanism to run it all.
We'll probably never know exactly what happened on Earth - the evidence has been wiped out, but we may be able to work out how it could have happened
http://en.wikipedia.org/wiki/Abiogenesis has an overview and a ton of references at the bottom.
One final thought - basic life appeared realy really fast on Earth (almost as soon as the early bombardment phase stops) which makes it look as if life probably starts quite easilly. It was another 3 billion years before complex life appears. That required the capture of one life form (mitochondria) by another.
This was an unbelieveably important event and catapulted life from being not much more than slime.
It may have been an amazingly improbable event - we don't know - there's only one example to look at.
The Universe is probably full of life - if that life is more than lichen - I'm not yet decided