Is there any chronological way to watch the Evil Dead franchise?

Not to step on the feet of the other answer that is also correct, consider this partial (Also, I hope I have not put any spoilers in..):

chronological way to watch the Evil Dead franchise?

Yes, pretty much as they were released.

Note the following:

Once the third film was released it was known as "the Evil Dead trilogy", from The Evil Dead, through the Evil Dead II and Army Of Darkness.

And pretty much has stayed this way ever since.

Given my additions at the end regarding the newer items:

TL;DR:

As in the other answer:

1. The Evil Dead

2. Evil Dead II

3. Army of Darkness: The Medieval Dead

4. Within The Woods - if the originals really gripped you, maybe the teaser short to sell the idea might be of interest. (Optional)

5. Then tv series as it has the same character, set thirty years later after the original trilogy.

6. Then 2013 last, as it has different tone - (from someone else) "..the originals had obvious Lovecraftian mythos, the new one is very standard Judaeo-Christian demonology.."

Fan-based sources but:

https://evildead.fandom.com/wiki/The_Evil_Dead_series

The Evil Dead

Released in 1981, this is the first official film in the series. It introduces the series' protagonist, Ash, and the Book of the Dead and what it brings with it.

The Evil Dead II

Released in 1987, this is the film that introduced the series's trademark humor, while expanding on the horror themes of Ash's dealings with the Necronomicon and demons.

Official synopsis also relates to Ash surviving the previous encounter:

The lone survivor of an onslaught of flesh-possessing spirits

and:

After a condensed recap, Evil Dead II continues where The Evil Dead left off; with the Evil Force rushing towards Ash.

Notes regarding the second film (spoilers beware):

While Raimi and Campbell have stated that Evil Dead 2 was intended as a direct sequel, there are differences between the first movie and the recap at the beginning of the second: for example, the Necronomicon is destroyed in a fire by Ash during the conclusion of The Evil Dead yet remains intact in Evil Dead 2. The corpses of Ash's friends from the first movie are absent, and they are never mentioned. The cabin itself remains perfectly intact until the events of this film despite much of it having been destroyed in the original film.

https://deadites.net/evil-dead-films/army-of-darkness/

Evil Dead III: Army of Darkness is the third and final installment ... of the Evil Trilogy.

Both sequels have issues in contradicting each other, EDII's issues are noted above, and with AoD, the beginning does not quite reflect the end of EDII, though the period time shown still matches.

For completists sake, there is an addition that can be viewed before the first Evil Dead film, perhaps as a prequel:

'Within The Woods', a short that was made (to sell investors on the idea of "The Evil Dead" feature) in 1978, can be viewed as a prototype for The Evil Dead - it has a number of similar & virtually identical shots, sequences & actions to 'The Evil Dead'

https://www.bookofthedead.ws/website/within_the_woods_synopsis.html

Regarding TV series:

and regarding the 2013 film:

https://www.ranker.com/list/evil-dead-remake-behind-the-scenes/jack-morgan

End note:

I recall a friend explaining EDII to me back when it was released: The first was serious, this is like a remake but much more fun (and money!)! (and by the end of it we were really looking forward to the third instalment)..

Pretty much the release order.

• Evil Dead
• Evil Dead 2
• Army of Darkness
• Ash vs Evil Dead

The 2013 Evil Dead Reboot is also good, but doesn't feature Ash as a main character and is a little bit different compared to the original.