Two meetings vie for the title: The Oct 22, 1936 meeting in Philadelphia and the Jan 3, 1937 meeting in Leeds. Some feel that the Philadelphia meeting was a mere visit of NY fans to Philadelphia and that the true first convention was the Leeds meeting in the UK.
This seems like hairsplitting, because small affairs like the Philadelphia meeting have subsequently been called "conventions" without objection. But it is certainly true that the first convention in the UK was both larger and more organized than the earlier Philadelphia gathering.
Perhaps it would be fairest to say that the first thing that could be called a convention was held in Philadelphia in 1936, while the first thing that must be called a convention was held in Leeds in 1937.
See also Early Conventions.