It has the same DNA that they passed on, doesn't it?
Yes, it has the same DNA "they passed on", but not the "same" DNA as it parents, otherwise there would be no genetic difference that would result in the major morphology difference - the tail. Inherited DNA contains some mistakes (mutations) not present in the parental DNA - if a chimp was born with a tail it would likely be due to a mutation not present in its parents' DNA, since chimps don't normally have tails.
I guess my real question to you guys is, at what point in the family tree, or at what generation gap can you consider a new species born?
I'm not sure what you mean by "generation gap", but a distinction between two species is a failure to interbreed under normal (wild) conditions. Thus, if tailed and normal chimps interbreed, they are one species. If the tail presents some barrier to mating between tailed and normal chimps, even if just behavioral, then a "new species" has likely formed.