The Man-from-Mars Radio Hat (1949)
From the cover story of the 1949 issue of Radio-Electronics (formerly Radio-Craft) about the latest in portable audio technology, the Radio Hat.
Power is supplied by a tiny 8-ounce battery pack that fits into a pocket and connects to the set through a 36-inch length of thin 3-conductor wire. The appearance of the set is bizarre but strangely impressive, as seen in the photographs.Many more pictures, including the fetching lass from the cover, are available in the complete reproduction of the article. Your iPod may have a million songs on it, but has it ever stopped the rain? Sir it has not.At a glance, this "man-from-Mars" personal radio would appear to be a child's toy but after using it for a few hours, we began to see its possibilities.
For example, it is just the thing for baseball fans who want to keep up with the doings of the out-of-town teams while rooting for the home-town favorites in the local ball park. Followers of the sport of Izaak Walton will be wearing their radios as they head-rod and reel in hand-for a spot on the banks of the old mill stream. For beaches, hiking, bicycling, picnics, or strolling in the park, the Radio Hat will prove its worth to all who wear it.
The Radio Hat [SWTPC.com] (Thanks, BrianK!)

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Still I wonder, who'll stop the rain?
I think that the cover girl inspired Devo. This also appeared decades before the beer hat. Clearly, the ancients possessed many secrets which are yet lost to the ages.
And it comes in EIGHT COLORS!
Hot vacuum tubes in the rain? Yikes...
Popular Science blurb about this hat:
http://blog.modernmechanix.com/2006/02/14/sun-hat-has-built-in-radio/
Older (1930) radio hat:
http://blog.modernmechanix.com/2007/11/07/music-while-walking-with-radio/
That's about $67 today (using the CPI).
Oh, that mini-dipole antenna on the 1930 hat is priceless.
The X-Ray specs interfere with reception.
And now a radio can fit on a microchip inside a portable 2 oz. phone
Does the foil lining selectively deflect the alien/government/big business transmissions? I must know.
Plus it's always a joy to see a circuit diagram that features two valves, and even more of a joy to see those valves sticking out of a jaunty het.
Get with the program Simon. Everyone knows the HAARP scalar waves control the weather and the aliens are on our side against the Illuminati, sheesh.