Scott is partially right, and to avoid any confusion...this is a 2-sided "nope."
Part one: Scott's right.
Part two: I barely trained chins at all over the past 1.5 years. On the other hand, I regularly did sets of 10 on Pendlay rows with 220-280. Started doing chins again, and didn't really have as much trouble as you'd think. It's totally feasible to train the strength for bodyweight work with barbells. The problem is that while you are building strength, it takes form practice to get bodyweight skills to work for you.
If you've lost strength while lifting: You're doing it wrong.
Also: I agree, Scott's thoughts on running are pretty useful.