Here's a link to Volume One of a Three Volume Set of J.R.R. Tolkien reading (and singing!) the Lord of the Rings that has finally made its way into the public domain. The distributor has asked that I not hard-link to the files, so you'll just have to go there and get them.

Also, here's a bonus! The Hobbit audiobook! Here's the source commentary:

Out-of-print audiobook whose adaptation was authorized by professor Tolkien himself, this was originally put out in 1974 as a boxed set of LPs. In my view, this is pretty much the best adaptation of The Hobbit ever, rivaling even the terrific animated film adaptation. It owes its greatness to the wonderful music and simply amazing voice work of Nicol Williamson, who may be better known to some as Merlin from the film Excalibur. If there were a Criterion Collection for audiobooks, this would surely be be one of the first titles.

part I
part II