The case brings US anti-drugs laws into direct conflict with freedom of religion legislation, and also poses the question whether American law overrides US obligations to international treaties.
The nine Supreme Court justices must decide whether to side with the US government, which argues the tea is a dangerous mind-altering substance, could be diverted to recreational drug users and is barred by an international treaty.
Or the court may hold that a 1993 US law on religious freedom means that the church, O Centro Espirita Beneficiente Uniao do Vegetal, (UDV) deserves an exemption for the tea.
The church is an unusual mix of Christian and indigenous South American spiritual beliefs, and has around 130 members in the United States, mainly in western New Mexico.
UDV rituals involve sipping hoasca tea, made from the roots of two indigenous Amazonian plants, in communion.
The case arose in 1999 when US customs officers intercepted a shipment of brewed hoasca liquid from Brazil. Hoasca contains dimethyltryptamine, or DMT, which is a banned substance in the United States.
Thirty gallons (136 litres) was seized from the home of Jeffrey Bronfman, the head of the church's American chapter and a member of the famed Canadian whisky-making dynasty.
The US government argues that the tea should not be allowed into the United States because it is a health risk, it could be diverted to non-religious users and it is barred by the international 1971 Convention on Psychotrophic Substances, designed to stem drug trafficking.
But lawyers for the UDV disputed that the treaty covers hoasca, argued the substance had never been passed to outsiders and said US religious laws meant the church should be allowed to use the tea.
They also argue that hoasca produced only a mild nauseating effect, and accuse government lawyers of exaggerating the impact of the substance.
Nancy Hollander, a lawyer for the UDV from New Mexico, argued that the drug was being used simply to permit followers to practise their religion.
Justice Antonin Scalia pointed out that Congress has the right to override a treaty through domestic law - in this case, the Religious Freedom Restoration Act, enacted in 1999.
"Isn't it well-established that statutes trump treaties?" he asked.
But Edwin Kneedler, the US deputy solicitor general arguing for the government, said that the United States could not simply opt out of the 1971 protocol, if it wanted other states to crack down on drugs trafficking.
"I believe that complying with an international convention designed to prohibit the trafficking in drugs is in itself a compelling interest," he said.