Proteins are synthesized on ribosomes from mRNA copies of regions of the DNA. But ribosomes themselves are made up of proteins (and RNA). So how could the first ribosomes have arisen? Was there previously some other way of making proteins other than by ribosomes and mRNA?
Although I am of the same opinion as fpdx and the majority of scientists — that there was an RNA world in which the genetic material and the catalytic molecules were RNA (rather than DNA and protein, respectively) — there are some quite respectable scientists who hold a different view. As there is no proof for either viewpoint (and hence no correct answer to the question), it is important to present this alternative.
In brief, the alternative viewpoint is of a "proteins-first" world: i.e. the first proteins were made without ribosomes from chemical reactions in the "primeval soup". Only later did the contemporary and template-driven ribonucleoprotein machinery for making proteins evolve.
I do not know of an online source of arguments in favour of the protein-first viewpoint — an article by C. Kurland in Bioessays 32: 866–871,(2010) requires library access or purchase. However there is an on-line article discussing the objections to the RNA-world viewpoint, which, even though it argues against these objections, gives one an idea why the question cannot be considered settled. This is available at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3495036/#B57.
(A quick answer to a question that will be likely closed being not well focused on the physics of all this)
First: the ribosome translates mRNA into the chain of amino acids that eventually will become a protein. The ribosome is a huge complex, made of both proteins and RNA. RNA can have enzymatic activity like a protein: the ribosome is a Ribozyme.
This chicken or the egg problem has puzzled biologists, chemists and biophysicists for a while. The structure itself of the ribosome was the "smocking gun" for the model we have today: the RNA world. In few words: because RNA can act as a protein and it is so similar to DNA, probably our DNA-world (i.e. information stored on the DNA, work done by proteins, RNA between the two) emerged from a fully RNA-world, where RNA was responsible for both protein activity and information storage. How in detail all this happened by evolution, is probably the subject of several nobel prizes to come.