Nice little image:

http://www.usmilitariaforum.com/uploads//monthly_11_2014/post-2064-0-65216000-1416612289.jpg

A good explanation:

http://ask.metafilter.com/227369/Why-do-they-not-use-the-chinstrap-properly

TL:DR version: It was believed that if a soldier were close enough to a blast the shockwave would catch the helmet like a sail and the chinstrap could snap their neck or even remove their head entirely. A new helmet was introduced in the later stages of WWII with a release catch to counter this problem. An enemy who snuck up behind you could also use the chinstrap to strangle you.

I find it to be an interesting transition point for helmet technology. Previously, a sturdy chinstrap was an extension of the helmets protection - for example, the chain chinstrap on the bearskins of the Royal Guard Grenadier Guards are to protect the face against saber slashes. Suddenly they found themselves in a situation where this was a negative asset and had to not only design a counter but to battle the perception that chinstraps were actively dangerous.