how does evolution explain the unique chromosome structure of each creature?

That would have been a sudden shift. There is a process called balanced (recprocal) translocation where the chromosomes rearrange or fuse. The individuals with these translocations are capable of reproducing with an increased risk for non-viable offspring. The balanced pair must be passed in tandem, but can propegate. Some people have fused chromosomes (1 in 1300 for 13/14). They are not able to reproduce with the general population, but could theoretically reproduce with someone with the same fusion. If, in the expansion into a new territory (Founder Effect), a popualion with a male and a female with the same fusion were present, they could have viable children with the double fusion. Their children would be viable, and could only reproduce with a cousin with the fusion, but many in the population have it. In a further expansion, the fusion could become predominant.

Evolution is gradual, mutation is sudden. In the example I cited, the process takes a few generations, not one. The most important fact is that there is no way to tell chromosome number apart in the group. They are, in effect, a new species because of the incompatibilty in mating, but they are phentypically identical. Without DNA evidence, the abrupt transition leaves no trace.

Unique Chromosome

There are many instances in meiosis where 2 pairs of chromosomes can become fused thereby eliminating 1 pair of chromosomes. DNA is not a perfect record as there are thousands of base pairs of DNA that are called "junk" because they never express any trait or code for anything. Donkeys and horse have a differing number of chromosome pairs yet are able to mate and produce a mule! The fact that evolution is thought to occur over a long period of time has been debunked by university research but the word hasnt gone mainstream. When I was in college 8 years ago they were concluding a study of polar bears and their increased time on the water due to lack of food on land. They had "evolved" significantly more webbing between their toes for easier swimming in just 6 decades!

Variations in chromosome number are known to occur in many different animal species.

There are two potential naturalistic explanations for the difference in chromosome numbers - either a fusion of two separate chromosomes occurred in the human line, or a fission of a chromosome occurred among the apes. The evidence favors a fusion event in the human line.

Further discussion and evidence here:

http://www.gate.net/~rwms/hum_ape_chrom.html

humans can produce offspring with an additional chromosome, it's genetic defect called down syndrome.

I thought humans have 36 chromosomes.

Not many people are doing yahoo answers any more! No ones getting answers for anything!