No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.
A Google News search for "third amendment" returns seven articles, referring to amendments in Pakistan, India, the UAE, and Coatesville, Pennsylvania. None refer to the United States constitution.
In fact it would seem that the Third Amendment to the Constitution of the United States is one of the least controversial legal issues ever. The founding fathers objected, in the Declaration of Independence, to the billeting of British soldiers in civilian homes, and so were determined not to repeat the offense.
It may well be the only law that rabid opponents have accused neither William Jefferson Clinton nor George Walker Bush -- nor even Richard Milhouse Nixon or even Howard Brush Dean -- of violating as President, as Governor, as Boy Scout, or ever at all.
So if the presidential campaign of 2004 comes down to "Brush" vs. "Shrub" (which are anagrams!), at least both candidates will apparently be able to agree on not housing soldiers in the homes of unwilling Americans.
It is apparently not a violation to house soldiers in Saddam's old palaces, but it would be a hoot if someone made something out of objecting to it.