As my 1 year-old cat, named Chase, walks around the house, he will pick up one of his…

Without seeing Chase, it's hard to know why he's doing this but my first thought would be that he has something on his back leg or foot. In particular, I would look to see if he has anything stuck in between his foot pads...this is a prime spot to get litter stuck. If it continues, or you see other symptoms like limping, you may want to have him examined to be sure he does not have an injury or something else that may be making his leg uncomfortable.