Most sources say that ML, the language which introduced Hindley-Milner type inference, was invented in 1973. Its type system, however, was not described until 1977 or 1978. Milner's A Theory of Type Polymorphism in Programming says:
the polymorphic type discipline which we discuss here has been incorporated in the LCF metalanguage ML [2, 3], and has been in use for nearly 2 years. The compile-time type checker for this language has proved to be a valuable filter which traps a significant proportion of programming errors.
The paper was written in 1977 and revised in 1978, so “nearly 2 years” means 1975 or 1976. (References 2 and 3 are LCF and ML documentation, from 1977 and 1978; neither is on the net.) The 1972 LCF documentation (warning: bad partial OCR) doesn't mention the metalanguage, so I suspect the date of 1973 refers to when it was first added.
Without its distinctive type system, ML would have been an uninteresting ISWIM derivative (with dynamic type, or monomorphic static type?), hardly recognizable as the ancestor of all modern statically typed languages. So we should date it not from its first, rudimentary version, but from the introduction of its most important feature, circa 1975, or from its publication, in 1977.
Update August 2015: Uninteresting? What about exceptions and pattern-matching?