Linda Stephens, a retired school librarian, and another resident of Greece, N.Y., Susan Galloway, have waged a five-year campaign arguing that the town is violating the Constitution by beginning town board meetings with a prayer. (Heather Ainsworth/Bloomberg)

The chairman of the local Baha’i congregation concluded his prayer with “Allah-u-Abha,” which loosely translates to “God the All-Glorious.” A Jew offered a prayer speaking of “the songs of David, your servant.” And a Wiccan priestess, mindful of her venue in the town of Greece, N.Y., thought that Athena and Apollo were apt deities to call upon.

But they were the exceptions. Almost every other “chaplain of the month” during a decade of town board meetings in this Rochester suburb was a Christian, and more often than not called on Jesus Christ or the Holy Spirit to guide the council’s deliberations.

A federal appeals court said last year that such a “steady drumbeat” of Christian invocations violates the Constitution’s prohibition against government endorsement of religion.

Now, the issue is set to come before the Supreme Court. Next week — soon after the court’s marshal announces a new session with the phrase “God save the United States and this honorable court” — the justices will once again tackle the role of religion in the public square.

Few phrases in the Constitution have divided Supreme Court justices quite like the First Amendment’s Establishment Clause, which says simply: “Congress shall make no law respecting an establishment of religion.”

Some prohibitions seem obvious: There can be no official national religion, for instance. Government cannot compel Americans to identify with a certain religion, or any religion at all.

What has proven more complicated is defining the boundaries of religion’s inclusion in public life. Issues such as prayer in public schools, accommodation of certain religious practices, and the display of crosses, creches and other religious symbols have produced a series of constitutional tests for the court and case-by-case rules that please few.

Against this “messy” backdrop, said Richard Garnett, a law professor at Notre Dame, the court’s view on legislative prayer “is actually one of the clearer areas in the court’s Establishment Clause” jurisprudence.

The court decided 30 years ago in a case called Marsh v. Chambers that Nebraska had not violated the Constitution by employing a Presbyterian minister for 16 years to lead the legislature in prayer.

Former Chief Justice Warren E. Burger said “the unambiguous and unbroken history of more than two hundred years” of legislative chaplains weighed in Nebraska’s favor.

The very first Congress, which drafted the First Amendment, was led in prayer by a chaplain, and the House and Senate have continued that tradition since then. This is one reason that the Obama administration is siding with the town of Greece. The town and its supporters say there is no evidence that Greece violated the requirement, which emerged from the Marsh case, that so-called legislative prayer not proselytize nor denigrate another faith.

“This case can begin and end with Marsh v. Chambers,” said the brief filed by Greece, which is represented by the Alliance Defending Freedom.

That is what a federal district judge concluded when two Greece residents challenged the town’s practice.

Susan Galloway, uncomfortable with the sectarian prayers, and Linda Stephens, an atheist, had objected to sitting through the invocations after the board changed from its old practice of beginning the meetings with a moment of silence.

The board drew its volunteer chaplains from a list of churches in the town. It said anyone would have been welcomed but did not publicize the opportunity. The board neither created rules for the prayers nor screened them beforehand.

After the lawsuit was threatened, the town made more of an effort — that’s how the Baha’i representative and the Wiccan got involved — but all agree that the overwhelming number of prayers offered over the approximately 10 years covered by the suit were offered by Christians, and most contained direct references to Christianity.

When the case reached the U.S. Court of Appeals for the 2nd Circuit, a unanimous panel of the court said it was not enough to view the town’s actions through the lens of Marsh. Judge Guido Calabresi said the Supreme Court had ruled in a subsequent case involving a creche display that governments must be careful about practices “that have the effect of affiliating the government with any one specific faith or belief.”

Despite what may have been good intentions, Calabresi wrote, that’s what the town of Greece had done. By not reaching out to a more diverse group of prayer-givers or making clear that the prayers did not represent the town’s beliefs, the judges found, “the town’s prayer practice must be viewed as an endorsement of a particular religious viewpoint.”

The town and the Obama administration argue that putting the government in a position of monitoring the content of prayers would create more constitutional problems.

“Neither federal courts nor legislative bodies are well suited to police the content of such prayers,” wrote Solicitor General Donald B. Verrilli Jr. on behalf of the United States, “and this court has consistently disapproved of government interference in dictating the substance of prayers.”

But the brief for Galloway and Stephens, who are represented by Americans United for Separation of Church and State, said the court’s precedents require such prayers to be nonsectarian and that the town is asking for too much leeway.

It would “leave government officials and guest chaplains free to admonish and harangue citizens to participate in sectarian prayers — even those that promise eternal hellfire to religious minorities,” the brief for the women says.

The challengers also say another of the court’s tests — one identified with Justice Anthony M. Kennedy, often the deciding vote at the court — must come into play. That test asks whether or not a practice is coercive, requiring individuals to participate in a religious practice.

Town council meetings, they say, are different from sessions of Congress or a state legislature, where visitors are observers. People often attend council meetings because they have to, they say, in order to apply for zoning variances or be sworn into jobs.

Because the town of Greece does not require chaplains to refrain from asking the audience to join in the prayers or make their invocations more inclusive, the challengers’ brief says, religious minorities are “pressed either to feign participation in act of worship that violates their own beliefs, or to publicly display their dissent.”

As with any Establishment Clause case, the controversy from Greece has attracted an outpouring of amicus briefs. They ask the court, on one side, to overturn Marsh or to be more explicit about what it means that prayers must be “nonsectarian.”

That has prompted the Rev. Robert E. Palmer, the chaplain in the 30-year-old Marsh case, to file a brief noting that his prayers were nondenominational — meaning they didn’t favor his Presbyterian faith over any other Christian religion — but not nonsectarian.

On the other side, there are briefs urging the court to do away with its tests and rules that restrict the role of religion in public life. But that would require an agreement among the justices that has eluded those who have come before.

Many experts, such as Garnett, think the court will be reluctant to go that far. If the justices rely on arguments based on history and tradition, such as those that prevailed in the Marsh case, they are likely to leave the state of the law relatively unchanged.