In Chicago, it would be illegal.
It was legal in Chicago until a couple of years ago. The case went all the way to Illinois supreme court, which ruled that it was legal to photograph police in the course of their public duties.
Illinois, led by the Daley machine, promptly passed a bill making it illegal to photograph police in public.
On the positive side, I believe that there are only two or three states that have such legislation. Illinois, and I think (surprise, surprise) New Jersey are two.
Illegal to film public servants serving in public? Oh well then, you must not do it! Laws, like police, are always right and must always be obeyed.