Why can't I do pull-ups?

I'm about 220 lbs, and 6 feet tall. I know I'm overweight, but I'm actually in pretty good shape. I don't look fat at all, actually, I'm just not even fat. I can run about 4 to 5 miles non-stop, I can do about 30-35 push ups, and same for sit-ups, but I can't do a singe pull-up to save my life. Is this due to my weight, or are my arms not strong enough? Help!!