The Swiss mathematian Jean Bernoulli (1667-1748) discovered the rule in 1694.
The French Marquis G.F.A. L'Hospital (1661-1704) made an agreement with Bernoulli
where L'Hospital would provide Bernoulli with a salary and in return Bernoulli
gave his discoveries to L'Hospital.
See "A History of Mathematics" by Carl B. Boyer
[For those who wrote in, L'Hospital is the way it is spelled in Boyer's book.
I'll see if there are alternative spellings.]