I need to know the names of famous people, celebrities or otherwise
accomplished people, who were born with a caul, a membrane. Being born
with a caul is quite rare and I understand that there are some who
believe that being born with a caul portends future greatness.

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Liberace - American musician and entertainer
--------------------------------------------
  
"The showman, we are told (Pyron often refers to Liberace as "the
showman", or "the entertainer"), "entered the world still enveloped in
the delicate, transparent membrane of the birth sac. He was born with
a caul.""
  
http://www.findarticles.com/p/articles/mi_m0FQP/is_4494_129/ai_64909461
  
  
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James Couzens - Industrialist, banker, politician
-------------------------------------------------
  
"According to folk legend, a child born with a caul (fetal membrane)
covering the head will have good fortune in life. The legend proved
true for James Joseph Couzens, Jr. Born in Chatham, Ontario, on August
26, 1872, his mother, Eunice Clift Couzens, an English immigrant, kept
the caul in a silk sack, giving it to Couzens' wife when he married."
  
http://www.bookrags.com/biography-james-couzens/
  
  
-------------------------
Queen Christina of Sweden
-------------------------
  
"On Dec. 8, 1626, the emptyheaded but beautiful Maria Eleonora, wife
of King Gustavus Adolphus of Sweden, gave birth to a hairy infant
covered with a caul."
  
http://www.trivia-library.com/b/famous-ruler-in-history-queen-christina-of-sweden-part-1.htm
  
"According to Christina, it was her birth itself that set the stage
for her ambiguous attitude to the traditional feminine role, which
would remain a major theme throughout her life. Christina would have
heard the account of her birth from those adults who were present on
the occasion: "I was born with a caul and only had the face, arms and
legs free...."
  
http://64.233.187.104/search?q=cache:1x4KAxODxYwJ:www.sweden.se/templates/cs/Print_BasicFactsheet____4403.aspx+%22Christina+of+Sweden%22+caul&hl=en&ie=UTF-8
  
  
---------------------------------
Frank Albert Jones - Black artist
---------------------------------
  
"When he was a small child his mother told him that he had been born
with a veil over his left eye, and that this veil would enable him to
see spirits."
  
http://www.tsha.utexas.edu/handbook/online/articles/JJ/fjobn.html
 
 
---------------------------------------------------------
Kahlil Gibran - Painter, sculptor, inventor and craftsman
---------------------------------------------------------
  
"The year was 1922, and in the crowded Syrian-Lebanese immigrant
community of Boston's South End, a boy was born who family and
neighbors knew would be remarkable. He had been born with a caul--that
is, with part of the fetal membrane over his head...
 
(...)
 
Today, Kahlil Gibran is a wide-ranging painter, sculptor, inventor and
craftsman whose work is not easily categorized. Living in a Victorian
town-house in his native South End, he has designed a thermite-fueled
furnace that gives off only water and oxygen, and an aluminum tripod
so light, sleek and functional that the Museum of Modern Art in New
York bought three for its collection. He makes violins that
world-class musicians have played, and has built a vihuela, a
17th-century Spanish stringed instrument, inlaid with lapis lazuli and
mother-of-pearl."
  
http://www.saudiaramcoworld.com/issue/199605/talent.to.spare.htm
  
  
--------------------------------------------------
Lord Byron - Poet and member of the House of Lords
--------------------------------------------------
 
"George Gordon, better known as Lord Byron, was born with a caul and a
club-foot on January 22, 1788, in London."
  
http://teachers.edenpr.org/~rolson/ArcadiaWeb/Byron/Byron1.html
 
  
--------------------
J.G.Farrell - Writer 
--------------------
  
"J.G.Farrell (1935?1979) was born with a caul, long considered a sign
of good fortune."
 
http://www.nybooks.com/nyrb/authors/4528
 
 
--------------------
Lillian Gish - Actor
--------------------
  
"Lillian Diana Gish was born in a rather large two-story house at 219
Linden Avenue, October 14, 1893. She was born with a caul, and
according to her grandmother, this was a good omen."
  
http://www.nytimes.com/books/first/a/affron-gish.html 
  
http://www.nndb.com/people/002/000031906/
 
 
 
Search terms used:
caul membrane "born with"
"born with the caul" OR "born with a caul"

I could not have asked for a better answer. You done good!

This may be of interest to you:

http://healthlink.mcw.edu/article/901311432.html

Thanks so much, Pinkfreud, but I already had that one. :-)

mcCAULey culkin?

I can't help wondering: 

Is a female who is born with this condition a caul girl?

Holden, Phoebe, or D.J. Caulfield?

The following link and information may be of use to you. A person born
with a caul is referred to as a Caulbearer and there is much popular
maythology and confusion concerning what a genuine caul (also referred
to as the Veil)is. Both males and females botn with a caul are
Caulbearers.

The site address is www.caulbearer.org