Final answer:
A male with Klinefelter syndrome (XXY) has one Barr body in his somatic cells, due to the inactivation of one of the two X chromosomes present.
Step-by-step explanation:
A male with Klinefelter syndrome (XXY) would have one Barr body in his somatic cells. This is because in individuals with Klinefelter syndrome, each cell has more than one X chromosome, and to maintain a normal level of genetic activity, every X chromosome except one undergoes inactivation. This inactivated X chromosome is visible as a Barr body within the nucleus of each cell. In the case of a male with a typical Klinefelter syndrome karyotype (47, XXY), there would be two X chromosomes present, but one would be inactivated to balance the genetic dosage, leading to the presence of a single Barr body.