Is it possible to create a 100% identical copy of a chemical?
I agree with most of what the commenters and @jerepierre have written, with one or two exceptions.  


  Is it possible to create a 100% identical copy of a chemical?


If your question were asked in an introductory chemistry class, I believe most instructors would answer with a simple "yes", for the reasons outlined above.  On the other hand, if your question were asked in an advanced chemistry class, or perhaps in a court of law, then I believe the answer would likely be "no".  A frustrating dichotomy, but such is life.

Let me explain the "no" answer.  To begin with, realize that simple molecules carry deuterium and $\ce{^13C}$ at levels found in natural abundance. Next, note that the way an organism would synthesize a vitamin, hormone, protein, etc., is likely different than the way a chemist might synthesize it in the laboratory. The differences would lie in the raw materials used in the process as well as the actual synthetic pathway.  

Each step in a synthesis that requires breaking (or making) a carbon-hydrogen bond or a carbon-carbon bond will result in isotopic fractionation.  Simply put, $\ce{C-H}$ bonds and $\ce{^12C-^12C}$ bonds are easier to break than the corresponding $\ce{C-D}$ bonds and $\ce{^13C-^12C}$ bonds.  Therefore, if we repeatedly break some number of (they can be different or the same) C-H bonds and/or C-C bonds, then our final product will be enriched in molecules with lower deuterium and $\ce{^13C}$ content, the degree of enrichment being dependent upon the difference in the number of carbon-hydrogen and carbon-carbon bond breaking and bond making steps between the synthetic process as carried out within the organism and as carried out on the lab bench.  There may be further fractionation if the starting material used by the body has required C-H and/or C-C bond making and breaking and has, therefore, also suffered isotopic fractionation.  Such fractionation can easily be monitored through comparison of the mass spectra of natural and synthetic compounds.

In addition to this isotopic differentiation between synthetic and natural products, there will also exist a difference in reaction by-products and contaminants created in these two different synthetic processes.

Both methods (isotopic fractionation and by-product/impurity differences) could be used to determine if, for example, the testosterone in an athlete's body was produced naturally within the body or synthetically outside the body.  Also, we are probably all aware of various reports were a synthetic version of a drug (often illicit, but not always) naturally produced by a plant or metabolite has produced death upon administration due to toxic by-products produced in the lab synthetic route - clearly a different side-effect profile.

So in answer to your question, no, it is not possible to synthesize a natural product in the lab that will be 100% identical to the same material produced in a living organism.