Independent Play???

I am a mom of a just-turned 3 year old boy who refuses to play on his own at all. He has a younger sister who has already mastered the skill much better than he has. At first I thought I was being selfish because I wanted him to be able to play independently so I could get some things done around the house but then when I mentioned it to a number of friends and then my pediatrician I learned that this is a skill he should certainly have by now. Now to clarify-I can give him a specific puzzle/game that he chooses himself out of the cabinet and when he sits down to play with it, he almost immediately gets up and just wanders around the house. I have urged him to play with his toys and even tried to begin play with a certain toy/game and then allow him to continue with it but he seems unable or unwilling or both. I am beginning to get concerned that there might be something wrong developmentally or something else going on with him. Does anyone have any children who have acted the same way? Does anyone have any advice on how I can encourage independent play? Thanks!!!