The federal government, through the Agriculture Department's Animal and Plant Health Inspection Service, runs a lottery that costs $1,000 to enter, has 400 winners, and can pay off in hundreds of thousands of dollars.

This game of chance focuses around an unusual new government facility -- the Harry S. Truman Animal Import Center, located on a tiny island off Key West, Fla. It was built, an agriculture official said recently, at the request of U.S. cattle breeders who want to import cows and bulls that must be quarantined for up to five months because the countries from which they come have histories of outbreaks of hoof and mouth disease, which is fatal to the animals. Without the Truman facility, there would no way for cattle from these countries to come into the United States.

To handle the demand for use of the 400 places for cattle at the facility, Agriculture officials came up with the idea of a lottery. Breeders submit their names to be drawn from a barrel; each drawing allocates a place for one cow. The $1,000 charged for each head of cattle accepted is used to pay the operational expenses of the Truman facility.

A proposed rule, carried in the Oct. 14 Federal Register (page 67643), would require breeders to attach a check of $1,000 with the application to the lottery for each head of cattle they want to put at the Truman facility.

It seems that for the first two drawings, money was not required in advance. As a result, many of the breeders did not come through with their animals. With fewer than 400 animals on hand, the average cost of the current group in quarantine is about $6,824 an animal.

For the next drawing, scheduled for Jan. 6, 1981, Agriculture officials expect that, with the money in up front, those winning cattle are bound to appear -- or, at the least, the money on hand will pay the expenses for those that do.