I remember a paper one/two years ago from William C. Earnshaw group which succeed in making a HAC (Human Artificial Chromosome) to pass through a few mouse generations. I don't think it has ever been used in human though but yeah stability is one of the major problem (also to be sure the HAC doesn't interact with other chromosomes).
Currently it seems CRISPR is what is used for germline editing both in different species. In human, George Church lab has made a try but the paper is not yet published and there are rumours of success by Chinese groups but until the publications came out we don't really know...
The idea for using CRISPR is to edit the hESC and then to develop them in sperm or gametes which is far more easier to perform than modifying the embryo directly (hESC is easy to obtain and grow whereas embryo is far more difficult to obtain and there is not a lot available).
The best country for doing this kind of experiments right now must be China since they don't seem to have any problem in performing it. In USA some scientists have already called for a moratorium but we still don't know if it will be followed.