During the first set of events 2 years ago, there was an amazing template by /u/Gabocius that showed how someone could run a Fire BV Chieftain in Endless Delve: https://www.reddit.com/r/pathofexile/comments/kan7uj/easy_95_in_endless_delve_fire_bv_pob_template_41k/

Here is my attempt to recreate it in 3.19:

~~Original:~~ ~~https://pobb.in/bTf998ht1RP0~~
~~Update 1:~~ ~~https://pobb.in/sXgA4Ue3L2BC~~ ~~Changelog:~~
- Rerouted to make it easier to transition to DPS tree, at the expense of being further away from a cluster jewel node (which I don't plan to use anyway).
- Rerouted lower part of tree to be closer to a +30 dex node (losing a +10 dex node in the process, so a net +20 win)
- Added a note about Blood of Summer rusted sword below.
~~Update 2:~~ ~~https://pobb.in/N09sJZHAuFta~~ ~~Changelog:~~
- So many changes!
- Added 5 new trees with skill sets and some item sets.
- Many, many thanks to u/metalonorfeed and u/razzor1100 for the explanations and POBs below. I've tried to faithfully incorporate their work into the POB.
~~Update 3:~~ ~~https://pobb.in/q64qsa3fRxXH~~ ~~Changelog:~~
- Added manni2's Occultist BV from LOK SSF to the list. Since we had so many other ascendancies, it didn't feel right to leave out Occultist which is the most popular BV ascendancy.
Update 4: https://pobb.in/cTxgWltvJFC1 Changelog:
- On razzor1100 tree, switched from WIndow of Opportunity to Exceptional Performance.

I am not a build creator, but this template matched my preferred style of builds - start with a solid tree and then layer on gear. As such, all items are empty. I built it on top of the original trees which you can see in the POB for comparison.

Some notes/ideas (NOTE: these are out of date - see the notes in POB for more information):

Many, if not all, notes in the original thread still apply. I highly recommend reading through that.
At Level 80, we have 230k DPS and ~4k life with no gear against Guardian/Pinnacle. Not as high as the original template, but not unusable.
Dexterity is still an issue for Chieftain. We go right by a +30 dex node, and more are 2 points away. Try to get it on gear wherever possible.
I cannot figure out how to fit endurance charge generation into the build. That would provide a nice bit of additional survival, if you can figure it out.
- The Remnant of Empires shield would be one way to do so. Even though we don't invest in block, delve has a lot of smaller hits and so it may keep us at a steady 1-2 charges on average (maybe higher?).
- We are quite close to block nodes as well, including Glancing Blows if anyone want to go down that route.
I assumed that we will not get any cluster jewels. If you find something usable, we are right next to a large jewel socket.
I created two Level ~90 trees. Feel free to mix-and-match per your preference.
- Survival = 79% max fire resistance, 230k DPS
- DPS = 75% max fire resistance, 336k DPS
We don't invest anything in crit, but we are next to a lot of crit nodes so that is a possibility also. I didn't really explore that.
I think there are 3 weapons which look nice from the Endless Delve starter items:
- Fragment of Eternity dagger gives both crit chance and crit multi (but I don't know how to build around this). The power charges provide a nice boost to crit chance (to almost 30%)
- Scar of Fate claw provides life on hit with spells and 50% reduced cost of socketed gems, which is nice.
- Splinter of the Moon wand gives us cast speed and 32% spell damage, also nice.
- (Update 1) Just tested Blood of Summer in POB, and it provides a nice bump to cast rate with frenzy charges - would be an interesting choice as well.