Question: What's the longest time a team of five players can hard-CC (stunned etc.) a single enemy champion continuously by chaining their CC?

Answer: 
Indefinite.

For simplicity's sake we'll just use a team of 5 Lux. Lux Q (binding light, roots enemy for 2 seconds) has an 11 second CD maxed out. With 40% CDR that's a 6.6 CD. Rooting lasts for 2 seconds. Only 4 Luxes are needed for perma CC.

Obviously, with other champions that have multiple CCs, low CD CCs, etc, infinite CC is definitely possible.

In a real match, the way the game works, death or CC evasion is much more likely to happen than a really long CC chain.

EDIT: 
Okay, here's a full example.

We can have the target stand next to the enemy nexus so mana won't be an issue. This setup would only require 4 people.

```
Lux - 6.6 CD 2 CC
Morgana - 6.6 CD 3 CC
Udyr - 6 CD 1 CC
Leona 4.2 CD 1.25 CC

```
zilean ABOUT 30 sec with E Q W E Q W E Q W E Q W E Q W E Q W E Q W E COMBO Do those CC chains come even close to this?
Zilean CD 22 CC 29.5