Looking for a way to replenish the cash drained every time you fill up at the pump? Look no further than Dorchester Minerals LP (Nasdaq:DMLP), an oil and gas company that literally pays dividends right now.

Dorchester isn’t just a bet on a promising shale formation that will require millions of dollars to produce gas at some point in the future. This limited partnership holds leases in 573 counties in 25 states, and many of these are currently producing oil and gas that generate royalties and profits for holders of its limited partner common units.

This profit flows right into their pockets every quarter — without a tax bite. The ticker symbol features the “LP” for a reason — as a limited partnership, Dorchester can distribute profit directly to limited partners without paying any corporate income tax. Rather than facing double taxation, an investor in Dorchester just pays income tax on those dividends.

In fiscal year 2007, Dorchester collected $65.3 million in revenue and distributed a whopping $57 million to its limited partners.

On top of that, the price of the common units has tracked the recent gains in oil and gas prices, doubling in value from its 52-week low of $18.50 last August to its 52-week high of $36.49 last month.

The kicker is that Dorchester also has interests in a promising shale formation: the Fayetteville Shale in the eastern end of the Arkoma Basin in Arkansas. This shale play has drawn larger companies such as Chesapeake Energy Corp. (NYSE:CHK) and Petrohawk Energy Corp. (NYSE:HK), who have made headlines for their prospects in the Haynesville Shale in eastern Texas and northern Louisiana.

Shale is considered a non-conventional resource for natural gas because it requires sophisticated and expensive techniques such as directional drilling and hydraulic fracturing to find and produce the gas. However, high prices for oil and gas have made these resources desirable. The July 2 sale by Chesapeake of a 20% interest in its Haynesville properties to Plains Exploration and Production Corp. (NYSE:PXP) for $3.3 billion valued its total holdings in Haynesville alone at $16.5 billion.

Dorchester barely counts its Fayetteville Shale properties (less than 1%) in the 82.77 billion cubic feet equivalent of proven reserves it listed at the end of calendar 2007. Production is ramping up on its Fayetteville acreage, though, with 43 wells completed and producing, another 18 wells being drilled and 25 more permitted or proposed by the operators.

Dorchester’s proven reserves break down to 74% natural gas and 26% oil. They also break down in 61% royalty (where Dorchester does not have a working interest in the production) and 39% net profit interests (where it does have a working interest).

The company points to its long history of positive revisions on reserves, as well as new purchases, that enable it to replenish reserves lost through production each year. About 70% of its some 345,000 net acres around the country are still undeveloped.

Dorchester finances its working interest costs through cash flow and has written into its partnership agreement that it will take on no debt, aside from normal trade debt. It pays for acquisitions with cash or through the issue of new partnership units. With only 27 full-time employees, it keeps expenses to a minimum — $5 million in 2007.

This minimalist structure means that increases in oil and gas prices completely flow through to the limited partners. In fact, because fixed costs in the working interests remain the same even when the price increases, a 30% increase in gas prices results in a 36% increase in cash flow for distribution to the limited partners.

The distribution for the first quarter ended March 31, 2008, was $0.5723 per unit for holders of record April 21, payable May 1, compared with $0.4611 in the year-ago period. The net earnings for the period were $15.4 million for the first quarter of 2008, compared with $9.1 in the year-ago period.

With Friday’s closing price of $33.37, Dorchester has a market cap of $942 million, but has shot into investor awareness too quickly to attract any analyst coverage. As revenue from the Fayetteville play begins flowing through, this is likely to change.

Chesapeake, which has nearly two dozen brokers following it, currently has a high target of $101 a share, compared with its price of $63.52. Petrohawk has a high target of $80, compared with a current price of $47.90. Get the picture?