The Dow Jones Industrial Average (DJINDICES:^DJI) is known for containing nothing but the bluest of the blue-chip stocks. These are companies that are vital to our economy and are viewed as more resistant to the ups and downs of the market than your average stock.

As a result, when it comes to payouts, the Dow Jones Industrial Average contains some of the best dividend stocks on the market. Here are the three that will pay you the most.

AT&T (NYSE:T) has the best dividend yield on the Dow at 5.1%. The company, as it is today and in previous forms, has a 74-year history of paying a dividend.

One of the reasons investors can be confident in this dividend is AT&T's position in the wireless business. It holds a quasi-duopoly in wireless with Verizon Wireless, a position that allows the two companies to invest billions in upgrading infrastructure and keeping competitors at bay. As you can see below, despite the recession, AT&T and Verizon both still hold a captive audience for their products, resulting in little revenue variation. After all, could you give up your cellphone?

T Revenue (TTM) Chart

T Revenue (TTM) data by YCharts.

Speaking of Verizon Communications (NYSE:VZ), the former AT&T segment spun off when the government split up the monopoly is the No. 2 dividend on the Dow. Its 4.2% dividend yield is more than a 30-year Treasury bond pays, and the payout goes back to 1984, when Verizon was known as Bell Atlantic. After buying the 45% of Verizon Wireless it didn't already own, Verizon has a dominant position in wireless, setting up dividend payouts for years to come.

The pharmaceutical business has been through its ups and downs over the past few years, but Merck (NYSE:MRK) still holds the third-best dividend on the Dow with a 3.8% yield. The sector may be facing changes, but with a long line of pharmaceuticals, consumer goods, and animal health products, Merck is prepared to weather the storm. Investors could even see a boost if Merck spins off noncore assets.