Every workplace has its token annoying person. It would be okay if he or she does not bug you personally, but if it does come to a point that you are being badgered that you are distracted from working, then it’s time to take some action.
Be upfront. Pull the person aside and have a private talk with him or her. This might actually work. One reason that they continue to be annoying is that they are unaware of it. Just be kind and break it to the other person gently. Don’t let your irritation or anger show too much.
If you think you are not in the right frame of mind to do the talking, talk to someone close to the person and ask if he or she could intervene. Whatever you do, do not shame the annoying person publicly. No one, not even him or her, deserves that.
If this doesn’t work, call the attention of the boss. This should be the last resort as you do not want to trouble your supervisor with something that can be resolve at your level.