Square, the mobile payments service led by Twitter cofounder Jack Dorsey, is raising a new funding round that values the company at an impressive $200 million

TechCrunch says Sequoia Capital is leading the round after beating out some of Silicon Valley’s other top firms, including Kleiner Perkins Caufield & Byers and Benchmark Capital.

The San Francisco startup makes a credit card reading device that can be attached to your Android phone, iPhone, iPod Touch, or iPad. One of the big challenges for Square (and competitors like FaceCash) is recruiting businesses to use the service, but it’s trying to overcome that difficulty by offering the card reader for free, then charging a small fee on each transaction. Back in November, the company said it was processing millions of dollars in transactions every week.

Square may be facing some legal challenges, because Washington University professor Bob Morley, who says he developed the technology with Square’s founders, was recently granted a patent that’s key to Square’s business.

The company’s previous investors include Khosla Ventures, Google executive Marissa Mayer, Foursquare co-founder Dennis Crowley, Twitter co-founder Biz Stone, Digg creator Kevin Rose, and many others.

In February 2009, Jim McKelvey wasn’t able to sell a piece of his glass art because he couldn’t accept a credit card as payment. Even though a majority of payments has moved to plastic cards, accepting payments from cards is still difficult, requiring long applications, expensive hardware, and an overly complex experience. Square was born a few days later right next to the old San Francisco US Mint.

Today the Square team is focused on bringing immediacy, transparency, and approachability to the world of payments: an inherently social interaction each of us participates in daily. Square is backed by Khosla Ventures and a team of angels. Square, Inc. has offices in San Francisco (Product & Engineering), Saint Louis (Operations), and New York City (Risk & Partnerships).