Twitter may be the Next Big Thing. Heck, it may be worth a billion dollars. But is there really a market for a dedicated device that does nothing but tweet, all day long? Privately-held Peek is hoping so.

The company last week introduced TwitterPeek, a $100 device that connects you to your Twitter account on the go. There's no contract to buy, and accompanying wireless service is free for six months, and $7.95 a month thereafter. Spend $199, and wireless service is free for the life of your Peek account.

I'll admit to being tempted by Peek's offer, if only because I'm (a) an incurable Twitter addict, and (b) morbidly curious. Where's the market for TwitterPeek when Twitter is already so pervasive? Why compete with Apple (NASDAQ:AAPL), Research In Motion (NASDAQ:RIMM), Palm (NASDAQ:PALM), and Motorola (NYSE:MOT), whose smartphones may as well be built to tweet?

I've no idea, honestly. And yet, before we dismiss the TwitterPeek, let's consider history. Peek made headlines last year with a dedicated email and text-messaging device called the Pronto. TwitterPeek could become equally successful.

Here's why I think it won't: Text messaging is a distinct and sometimes-expensive service. As such, users have rushed to technologies that do texting on the cheap, such as Google's (NASDAQ:GOOG) Voice service.

Pronto operates on its own wireless network, and not surprisingly, has proven disruptive to telecom incumbents such as AT&T (NYSE:T) and Verizon (NYSE:VZ). TwitterPeek just tweets, and tweeting is usually free.

Where TwitterPeek could create value -- or so the company says -- is in sparing users data overage charges they might encounter using a phone. That's possible, but AT&T is now serving nothing but fixed-fee, unlimited data plans. T-Mobile is selling unlimited voice and data plans with no contract. Add it up, and Peek's data savings promise seems to be irrelevant.

But that's also just my take. Now it's your turn. Would you buy a TwitterPeek? Please vote in the poll below and then leave a comment to explain your thinking.

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Fool contributor Tim Beyers had stock and options positions in Apple and a stock position in Google at the time of publication. Check out Tim's portfolio holdings and Foolish writings, or connect with him on Twitter as @milehighfool. The Motley Fool is also on Twitter as @TheMotleyFool. The Fool's disclosure policy is too thumb-sore for tweeting right now. Perhaps later.