When Delaware U.S. Senate candidate Christine O’Donnell interjected this question in last week’s debate with her opponent Chris Coons, the audience—a law school audience—laughed and guffawed in derision. But the joke, of course, is on the audience: as everyone with even a modicum of understanding of the Constitution knows, the term “separation of church and state” appears nowhere in the Constitution. Even Mr. Coons acknowledged as much. The metaphor of a “wall of separation” comes from a letter President Thomas Jefferson penned to a group of Baptists in Danbury, Connecticut—a dozen years after the Constitution and Bill of Rights were ratified. The phrase is not mentioned in the Constitution’s text or in any of the debates leading to its ratification.

What the Constitution’s First Amendment does say is that government shall make no law “respecting an establishment of religion or prohibiting the free exercise thereof.” It is well to attend to the actual words of the Constitution (an admirable obsession of some Tea Party folks, like Ms. O’Donnell). Nowhere is this more important than with the Establishment Clause of the First Amendment: forbidding an official establishment of religion is something quite different from the much looser, imprecise term “separation of church and state.” The Constitution only forbids government sponsorship and compulsion of religious exercise by individual citizens. It does not require hermetic “separation”—implying exclusion—of religion and religious persons from public affairs of state.

A strict separationist view is not supported by the Constitution. Indeed, such an approach would contradict other parts of the First Amendment, in important ways. Most obviously, it would be at war with the protection of the “free exercise” of religion. If government could wall out religious persons and groups from participation in public affairs or from benefits or programs generally available to all, on the basis of neutral criteria, that would mean government could discriminate against religion. It is utter foolishness to think that the framers of the First Amendment intended such a result—and wrote an incoherent guarantee of religious liberty that contradicted itself in the same sentence, both requiring and forbidding discrimination against religion in one breath.

The strict separationist view is also at war with the freedom of speech and press, likewise protected by the First Amendment. Under a “separation” view, religious groups could not use government facilities (school buildings, public parks) for expressive purposes on the same basis as other groups. Literally dozens of Supreme Court cases reject that view. In a notable 1995 case (Rosenberger v. University of Virginia) the Court held that a state university could not refuse to fund on an even-handed basis a religious student newspaper, if it made funding available to other student publications. The Free Speech Clause forbade discrimination against religious speech or press, the Court held, and the Establishment Clause could not sensibly be read to require such discrimination.

The correct understanding of the First Amendment is not that it forbids contact—and even voluntary cooperation—between church and state. Rather, it protects private religious liberty, but does so in two complementary ways. In a nutshell, government may neither compel nor prohibit religious exercise. The Establishment Clause side of the coin says that government may not prescribe religious exercise; the Free Exercise side says that government may not proscribe, disfavor or otherwise punish or prevent religious exercise voluntarily chosen by the people. But the two phrases are two sides of the same coin. It is little wonder, then, that the Supreme Court has abandoned entirely the misleading metaphor “separation of church and state.” It simply does not help explain the true meaning of the First Amendment.

This is more than a quibble. The different understanding makes a difference in results. Under a separation view, government must discriminate against religion, reject school choice “voucher” plans that include religious options, and extirpate religious references and symbols from public discourse. Under the original meaning of the Constitution, government must protect religious choices and include religious persons, groups, and speakers on an equal basis. It may recognize and accommodate religion, as long as it does not in effect compel persons to engage in religious exercises or practices against their will—the hallmark of what an “establishment of religion” was understood to mean at the time the framers wrote the First Amendment.

Ms. O’Donnell’s pithy challenge—“Where in the Constitution is the separation of church and state?”—is actually an excellent shorthand critique of those (like Mr. Coons, perhaps?) who would sloppily translate the First Amendment’s protections of religious liberty into incoherent hostility toward religion. And that is no laughing matter.