Here’s another good response from Mithrandylan in an email correspondence on the same subject (with permission):
Depends on what you mean by chronological order. If you mean chronological publishingorder, it's: (I'll give my recommended "event-based" chronological order after)
LOTR (published ~15 years after The Hobbit)
Only those two, plus I think The Adventures of Tom bσɱbadil, were published during his lifetime. The rest were published posthumously, in this order:
The Silmarillion (mid-late 70s)
Unfinished Tales of Numenor
The History of Middle Earth (80s-- Book of Unfinished tales vols 1-2, Lays of Beleriand, Shaping of Middle Earth, The Lost Road)
The History of the Lord of the Rings (late 80s-early 90s; four or five books dealing with extant LOTR stories and details surrounding the War of the Ring--The Return of Shadow, The Treason of Isengard, I forget the other two or three)
Morgoth's Ring (early 90s, deals with extant Silmarillion material)
The War of the Jewels (early 90s, also extant silmarillion material)
The Children of Hurin (mid 2000s)
Beren & Luthien (2000s)
The Fall of Gondolin (2010s)
All the posthumous works were edited by Christopher Tolkien, one of Tolkien's sons. Tolkienites-- lay and scholarly, Catholic and secular-- aren't pedantic about this. Christopher Tolkien didn't do much editorializing or changing, and those other works read like LOTR does (though not like The Hobbit does-- The Hobbit was written for children, reads much more like CS Lewis compared to LOTR which is written for adults and reads more like an epic novel). Christopher (more or less) just compiled his fathers copious notes, made connections, filled in any necessary blanks, etc.
Although there is technically a strict chronological order in which the books could be read based on the chronology of Middle Earth events, I'm not sure how enjoyable a read it would make. It would involve jumping back and forth between books like The Silmarillion, Children of Hurin, Unfinished Tales, etc. The SIlmarillion deals with some of the earliest events in Middle Earth, whereas some of the other books focus in on specific events that happened aroudn the same time, are mentioned in the Silmarillion, but not delved into in considerable detail. Perhaps obviously, if one were to read MIddle Earth books in strict chronological order, one would finish with The Hobbit and then LOTR.
If you haven't read any LOTR materials, this is my strong recommendation: start with The Hobbit. Read it with your kids, if you think they could understand (it is, after all, a children's book a la CS Lewis's Chronicles of Narnia and reads as though your grandpa is telling you a story by the fireplace). If you like it, then read the LOTR trilogy (probably not with your kids, since it's written for a more adult vocabulary-- not that there's anything inappropriate, it just probably will go over the heads of kiddos). If you make it through LOTR and The Hobbit, read the appendices at the end of Return of the King. These deal with some important history of Middle Earth (they are actually fairly long, as a matter of fact) and are written in the (often-criticized) dry, historical, quasi-scholarly tone that one encoutners when reading The Silmarillion. If the appendices are to your liking, then you know that you should keep on going with the material edited by Christopher Tolkien, and you'd start with The Silmarillion, tthen probably go to UNfinished Tales. Children of Hurin will enkindle your inner Greek tragedian, and if you're into that kind of thing (I certainly am), read that too-- after Unfinished Tales, probably. Ditto Beren & Luthien and The Fall of Gondolin.
So far as the HIstory of Middle Earth and HIstory of the War of the Ring series' are concerned, they're non-imperative. They take on a historical-summary tone and therefore are more useful for reference than for an actually enjoyable reading experience. They exist to annotate history, not to tell stories. You could skip them, since the meat and potatoes of them is included in other books. Unless, of course, you're planning a career change to a Tolkien-scholar.