When did Visa become a publicly traded company?

18th March 2008.

As per Wikipedia:

On October 3, 2007, Visa completed its corporate restructuring with the formation of Visa Inc. The new company was the first step towards Visa's IPO.[28] The second step came on November 9, 2007, when the new Visa Inc. submitted its $10 billion IPO filing with the U.S. Securities and Exchange Commission (SEC).[29] On February 25, 2008, Visa announced it would go ahead with an IPO of half its shares.[30] The IPO took place on March 18, 2008. Visa sold 406 million shares at US$44 per share ($2 above the high end of the expected $37–42 pricing range), raising US$17.9 billion in the largest initial public offering in U.S. history.[31] On March 20, 2008, the IPO underwriters (including JP Morgan, Goldman Sachs & Co., Banc of America Securities LLC, Citi, HSBC, Merrill Lynch & Co., UBS Investment Bank and Wachovia Securities) exercised their over-allotment option, purchasing an additional 40.6 million shares, bringing Visa's total IPO share count to 446.6 million, and bringing the total proceeds to US$19.1 billion.[32] Visa now trades under the ticker symbol "V" on the New York Stock Exchange.[33]

Source: Visa Inc.