Spokeswoman Barb Maynes said officials are monitoring the building by air until someone is able to hike in.
The chalet was built in the early 1930s and used as a lodge for hikers and horseback riders. Its now mainly used as a summer ranger station and emergency shelter.
The Peninsula Daily News reported it was added to the National Register of Historic Place in 2007.
The structure is located in the southwest corner of the park, 13 miles up the Graves Creek trail in the Enchanted Valley, a designated wilderness.
Information from: Peninsula Daily News, http://www.peninsuladailynews.com
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