To start with, in the test tube, human sperm don't bind to the receptors on a chimp egg. And even if they did, or you used in vitro fertilization to directly inject the sperm into the egg, the chromosomes wouldn't pair up. Humans have 46 chromosomes while the other apes have 48 chromosomes. Sometime, way back when, on the way to Homo sapiens, the monkey chromosomes 11 and 12 fused to form what is now human chromosome 2. There are also eight major inversions in human chromosomes when you try to match them up with chimp chromosomes. Chromosome pairing is necessary for fertilization
and the development of the egg.
Which brings up the question, after the first chromosome 2 fusion occurred, how did it get passed on? Chromosome events like these often (but not always) tend to reduce fertility, although viability may be unchanged (or even improved). These low probability events can be fixed, especially in small inter-breeding populations. But after many changes have occurred between the chromosomes, the possibility of interbreeding ceases, and a new
species has been created. As a matter of fact, loss of ability to
interbreed is one of the functional definitions of a species.