Credit:
Although there have been Twitter promotions from many companies before (they've proven successful enough that they keep coming), this one is distinguished somewhat by the use of TwitPic. Other promotions have just asked you to retweet something to receive a prize.
The idea is that a little more involvement and creativity should go a long way, and when you participate you provide Dentyne free exposure to all your followers. A person who is very concerned about his or her Twitter image probably won't participate for fear of being labeled a spammer, but your average Twitter user won't have any qualms about it.