Yes, working out with soreness is okay, when proper rest was given--as long as its delayed onset soreness. Sometimes stretching, etc, and getting the old stale blood out and in with some new, will lesson the soreness.
To this very day, my chest muscles get sore after a workout ( I dont mess around in the gym

), off all my muscle groups, it is the one that can take the LEAST pounding (so, if it takes less,,,,,great!, I just back off and do less to get the job done in accordance to what my body is telling me)
As long as its not something else, working through soreness once in awhile will not hurt you.......just give proper rest, and have proper diet.