As the chimes from a distant church rang the noon hour over the Shaw neighborhood in Northwest Washington yesterday, 80-year-old Zola Sessions was hobbling homeward, one well-wrinkled hand tight on the crook of her aluminum cane and the other bringing home the cheese.

Yesterday, for the second time since December when President Reagan ordered that the nation's needy be given thousands of tons of surplus government cheese, Washington's poor stood in line for the one-to-a-family, five-pound blocks of processed American cheese.

This time those lines were short, almost as short as the time people had to wait. About 3,300 people were given cheese, according to the Rev. Ernest R. Gibson, director of the Council of Churches of Greater Washington, which coordinated the giveaway. "It went well," Gibson said, "apparently without a hitch."

When the Council of Churches of Greater Washington distributed 18,000 pounds of the cheese in January, hundreds of those who stood in the winter's cold were turned away--disappointed, angry and without cheese.

Sessions said she had heard about all that trouble last time, so she decided she'd walk to her neighborhood distribution center, the United House of Prayer at Sixth and M streets NW, two hours before the scheduled noontime giveaway.

It wasn't necessary. Cheery-faced volunteers saw to that. The elderly, those on welfare, the unemployed, entered the church's basement auditorium four at a time. They passed through a battery of checkpoints, where they presented Medicaid cards, food stamp receipts and other papers to verify their need, before coming to a long table stacked high with brown cardboard boxes of cheese.

Sessions was pleased moments after she buried her cheese deep in her plastic shopping bag. "I need it," she said, "plus, I never got anything free in my life. I appreciate it so much."

A sign of the times was the estimated value of the cheese. In January, the five-pound blocks were valued by retailers as being worth $11 each. Yesterday, food store clerks said a five-pound block of cheese would sell for more than $13, an increase of about 15 percent over three months.

Gibson said things went smoothly yesterday because organizers had more time to plan, and because lessons were learned from the first effort. Instead of six churches, 13 were used to hand out the 17,100 pounds of cheese.

Gibson said, however, that some were turned away--at least 35 at his church, the First Rising Mount Zion Baptist Church at Sixth and N streets NW.

Gibson said he is appealing to D.C. officials to help the council secure other foods such as flour, meat, beans and milk to give to the city's poor. The next cheese giveaway is tentatively set for April 28, he said.