The French Wikipedia article History of the normal distribution is quite precise on that question (translation mine):
The first table ever made was by Laplace in 1778 who was using the normal distribution as an approximation to the hypergeometric distribution, and that table got published in 1781.
Does anyone know where to find a scanned version of that table, or any other kind of support for this fact (other than the given reference book by Yadolah Dodge which cannot seem to be found online)?