Taliban spokesman Qari Yousef Ahmadi claimed responsibility on behalf of the insurgents, saying militants shot down the helicopter with two rockets.
Helmand provincial government spokesman Daoud Ahmadi said the attack occurred about midday in Sangin province.
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Both U.S. and British troops are operating in Helmand, part of a band of provinces across southern Afghanistan that are the Taliban's heartland.
Obama last December ordered some 30,000 more U.S. troops to Afghanistan, and most of them are due to be deployed in the south.
U.S. commanders are planning a major operation in Kandahar that they hope will turn the tide of the war in time for American troops to begin withdrawing on Obama's stated timetable starting in July 2011. Helmand province abuts Kandahar.
Insurgents have stepped up attacks ahead of the Kandahar operation. The spike in violence has killed 28 NATO troops this month, including Wednesday's casualties.