This topic has been discussed many times over on the interwebz, but I thought I'd just add my own explanation of it anyway...
A valid question one might ask about the evolutionary relationship between humans and chimpanzees is this - why do the human and chimpanzee genomes have different numbers of chromosomes when evolutionary theory insists that we are so closely related?
The story of how this apparent stumbling block was resolved is one of the greatest triumphs for evolutionary theory over ID/creationism.
The Great Apes, as in chimps, gorillas and orangutans, have 24 pairs of chromosomes compared to 23 pairs in humans. This has been known to be the case since the 1970s. Back then, it was a potential problem for evolutionary theory, because it had to be explained how there was a difference between these related species.
Creationists, of course, were happy that the numbers were different. This confirmed for them that humans are unique and were designed with 23 pairs of chromosomes. Evolutionists, on the other hand, came up with a testable hypothesis (real science) to explain the differences...
One initial possibility was that humans may have lost a pair of chromosomes following divergence from the rest of the Great Apes, but this was widely ruled out as loss of whole chromosomes would almost certainly be fatal. So the generally accepted hypothesis was that two chromosomes must have fused together to form a new longer chromosome, thus reducing the number of pairs from 24 to 23. The implication of this, of course, was that if no evidence of a fusion event could be found, then evolutionary theory would be in big trouble.
Wild Horses 66, Domestic Horses 64, and Donkeys 62 Chromosomes
When I confront creationists on the issue of Human/Ape chromosome numbers, I use all the science mentioned in this blog, plus I add information from the genus Equus.I first ask creationists if Horses, Donkeys, and Zebras are related. They often reply “yes, they are of the same created kind”, often noting that Horses, Zebras, and Donkeys can breed with each other and that they are all descendants of the 2 horses on Noah’s ark 4000 years ago. Then I reveal their chromosome numbers.
Wild Horses (Equus ferus przewalskii) have 66 chromosomes. Domestic horses (Equus caballus) have 64 chromosomes, and Donkeys have 62 chromosomes. The cross of a domestic horse and a donkey produces a mule or hinney with 63 chromosomes. Crossing a wild horse with a domestic horse produces a horse with 65 chromosomes.
If Equus species that range in chromosome number from 62 to 66 can all descend from a common ancestor, why can’t apes (48 chromosomes) and humans (46 chromosomes) descend from a common ancestor?
I also ask them if any humans have more than 46 chromosomes. Every time but once, they have said no. Then I inform them that people with Down’s Syndrom have 47 (due to 3 copies of chromosome 21).
Successful reproduction in individuals with different chromosome numbers is also known to occur in humans, as is seen with individuals with a Robertsonian translocation (a disorder where a full or partial chromosome fuses to another). More than 1 in 1000 people have Robertsonian translocations and can still reproduce successfully. Not all of their offspring will survive, but some will, which is all that matters. I'm not going to get into the Mendelian genetics of it, but its roughly a 1 in 4 survival chance. Now, the offspring with the same fusion (it will be passed on to 50% of the viable offspring) will have the same fertility as the parent, so will also be able to reproduce with a 1 in 4 chance. And so on...
Here comes the amazing bit...
Think back to our ancestor who had the original fusion event. Following generations of reproduction, the individuals with the fusion event would slowly accumulate in a population, although still be a minority. When two individuals with the fusion event mate, because they have identical chromosome numbers, they will have 100% fertility. This 4-fold increase in fertility will cause the population with the fusion event to continue to mate with each other. Similarly, the larger population without the fusion event will prefer to mate with each other, and not the new population.
As I hope you can see, this would potentially contribute to reproductive isolation and the beginnings of speciation...!
So the fact that we have different chromosome numbers to the Great Apes has been lucidly and elegantly explained by evolutionary theory. This was done by making a testable hypothesis and then doing the research. Contrast that to the complete lack of an explanation or research from ID creationism. Fusion events have also been observed in the genomes of other mammals, and always verify expected lineages. An excellent additional bonus is that it provides us with a potential reproductive explanation for speciation.
*Ahem*
Pwnage.