If South Africa continues to shun the chickens of America to protect its own, officials say, then perhaps that nation should be removed from the trade agreement that allows it to send its wines, luxury automobiles and other goods here.

“You want unlimited access to American market to sell autos, yet you won’t let my state send its biggest agriculture export into your country?” fumed Mr. Coons, who has long been involved in African affairs.

The dispute over chickens comes just as President Obama is pushing an aggressive trade agenda in Congress. But for some lawmakers the rejection of American chicken is emblematic of other disputes, and evidence that trade agreements often do not live up to their billing for the United States.

“Members of Congress are fed up with this,” said Representative Rosa DeLauro, Democrat of Connecticut.

The African Growth and Opportunity Act, a trade deal providing duty-free treatment for some products from sub-Saharan Africa, was first passed in 2000 to help bring that impoverished region into the international economy. That was the same year South Africa — which accounts for the majority of American imports under the trade deal and which exports billions of dollars in goods to America — began to impose large duties on chickens, which officials here believe is a trade violation. South Africa contends that the United States is trying to “dump” chicken on its market below the cost of production.

For several years, questions have been raised about the need for the inclusion of South Africa, a member of the Group of 20 largest industrial economies with a booming middle class.