Can I boil pasta in the same water/broth that I boiled chicken in?

Yes, just make sure you have enough liquid. Pasta should be cooked with the ratio of 1 gallon of liquid (normally water) per 1 pound of dried pasta. Technically 1 oz of salt is also needed per gallon of water to properly season your pasta. I would strain the cooking liquid to get rid of any debris left by the chicken or it will latch onto your pasta leaving it kinda funky. Another thing to worry about is the amount of dissolved gelatin in the cooking liquid, which may conflict the proper cooking of your pasta.