FORT WORTH — The 3-year-old boy who could upend a 40-year-old law aimed at protecting Native American children barreled into the suburban living room, merrily defying his parents’ prediction that he might be shy. He had a thatch of night-black hair and dark eyes that glowed with mischievous curiosity. As he pumped a stranger’s hand and scampered off to bounce on an indoor trampoline, his Superman cape floated behind him, as if trying to catch up.

Zachary, or A.L.M. as he is called in legal papers, has a Navajo birth mother, a Cherokee birth father and adoptive parents, Jennifer and Chad Brackeen, neither of whom is Native American. The Brackeens are challenging a federal law governing Native American children in state foster care: It requires that priority to adopt them be given to Native families, to reinforce the children’s tribal identity.

Last fall, a federal judge ruled in the Brackeens’ favor, declaring that the law, the Indian Child Welfare Act, was unconstitutional — in part, he said, because it was based on race.

The case is now before a federal appeals court. Whoever loses is almost certain to ask the Supreme Court to hear it.