On a TV show I saw within the past two hours, a fellow named David
Barton mentioned a situation where undercover police (I think he said
in Alabama) are going to a school cafeteria to make sure students
aren't praying over their lunches.  In his view, of course, this is
just another example of government-sanctioned godlessness.  I have
been unable to substantiate Barton's story, and I strongly suspect it
is either an urban legend, a fabrication, or a gross distortion of an
actual event.  I'd like to know the origin of the story and to know
what really happened.  (If the answer is that the story is a
fabrication, I'll need some evidence of that; just saying "that
couldn't have happened because it's unconstitutional" isn't enough.) 
Thank you.

Hello.

In the 1997 case of Chandler vs. James (later known as Chandler vs.
Siegelman), U.S. District Judge Ira DeMent of Montgomery, Alabama,
issued an injunction requiring that "monitors" check for violations of
an order barring government-sanctioned religion in DeKalb County
public schools. See the order on the web site of the American Civil
Liberties Union (ACLU):
http://www.aclu.org/court/alabama_injunction.html

According to the injunction, "The monitor shall have the power and
authority to: (i) enter any classroom or public school property,
school assembly, sporting event, commencement exercise, or
school-sponsored or school-initiated event for the purpose of
observing and reporting on compliance for the duration of this
PERMANENT INJUNCTION"

Judge DeMent's original ruling contains a general summary of the facts
surrounding the case. It's also on the ACLU site:
http://www.aclu.org/court/alabama_decision.html

More discussion of the "prayer monitors" from the ACLU site:
http://www.aclu.org/news/w120897b.html

Other orders made by Judge DeMent in the case:
http://www.aclu.org/issues/religion/alabamaspec.html

The portion of Judge DeMent's injunction that involved prohibition of
student-initiated prayer was overturned in July 1999 by 11th Circuit
Court of Appeals. See their ruling courtesy of Emory University:
http://www.law.emory.edu/11circuit/july99/97-6898.man.html

The 11th Circuit revisited the matter in 2000 & 2001. See their
rulings also on the Emory page:
2000
http://www.law.emory.edu/11circuit/oct2000/97-6898.ma2.html
2001
http://www.law.emory.edu/11circuit/apr2001/97-6898.ma3.html

In July 2001, the U.S. Supreme Court declined to hear an appeal of the
11th Circuit's ruling. There's a brief report on the web site of
Education Week:
http://www.edweek.org/ew/ewstory.cfm?slug=42scotus.h20

The bottom line is that, yes, monitors were appointed in Alabama to
make sure that the schools weren't sponsoring prayer, but, no,
undercover cops aren't busting kids for praying in the cafeteria.

search strategy: alabama, school, prayer, police

I hope this helps. Good luck in your research.

Informative, thorough answer. I had run across the same case in my
research but didn't make the connection.