This build is optimized for 2 things:
-Maximizing your allies pottential.
-Making your enemies hate life.

With the ammount of slows and stuns you can output, enemies will barely be able to play, while allies are mostly free to do anything.
This forces enemies to try and focus you, but you are pretty tanky yourself, so focusing you is actually a terrible decision, which means that no matter what they try to do...

It is just according to keikaku.

You'd at first think it weird for a Chemtank on Zilean, but its active is absolutely perfect for your engage, while the tankyness it gives is extremely welcomed.

By starting an engage with Chemtank, you have almost 100% certainty of hitting your bomb stun while keeping enemies being damaged non-stop for years by your adc, yet it can also be used to escape enemies and even gives you a per second damage for any enemies that try to wait around your body while you resurrect.

Engage:
Chemtank + E(Self) > Chemtank slow > Q > AA > W > E(Enemy) > Q > AA > Exhaust

Medium range:
E(Enemy) > Q > AA > W > E(Enemy) > Q > AA

With Randuin's:
Chemtank > Q > AA > E > W > Q > AA > E > Randuin's > Exhaust

The Miracle Dash:
Chemtank + E(Self) > W > E(Self) > Flash > R(Ally) > Exhaust
(+1 Honor)

With both Chemtank and Rylai's, not only will you be ever present and difficult to deal with, your presence alone will feel like time slowing down for your enemies and speeding up for your team, as Zilean is supposed to.

The amount of cooldown reduction on the build also makes your ultimate's cooldown extremely tiny, yet the amount of AP still make sure that you hurt, badly, even though you can tank quite a lot.

By the time you have Warmog's, enemies will make sure to at least try to avoid fighting wherever you are, but due to your move speed, you will basically be everywhere around the map and your engage with Chemtank is NASTY.

While the Wardstone makes it so that you have so much CDR and vision control, the map almost always will belong to your team, denying your enemies even vision.

Depending on who your teammates ar, or if you feel uncomfortable with Chemtank, you can swap it for a Shurelya's Battlesong.

Instead of slowing enemies down, you will speed your team up.
This is good for teams with Kled and/or Sivir or champions that get a lot of benefit from movespeed, like Hecarim.

Your main engage combo would become:
Shurelya's > E(Enemy) > Q > AA > W > E(Enemy) > Q > AA > Exhaust.

If instead you choose to go for the Everfrost, you will lose your engage movement speed combo will become mid ranged.
Everfrost Combo:
E(Enemy) > Q > AA > W > E(Enemy) > Q > AA > Everfrost > Exhaust > Repeat