Yes. Millions of years ago, chemicals formed together to create a single cell. This unicellular organism was able to stay alive because the chemicals reacted in a way that could carry out the 8 life processes. The cell reproduced and soon mutations led to variation in the species. This evolution has continued to the present day.
This is the current basis of evolutionary theory, yes. Also, there are many single-celled organisms still present on earth, so the idea isn't all that hard to believe.
There is evidence to support a theory of evolution that would conclude life evolving from a single cell. However, as a theory, its truth has not yet been proven scientifically.