The Chaos Gambit is a story mission in South Park: The Fractured But Whole.
Plot details follow.
To start this mission, meet up with the team at the Coon Lair. Then, after the cutscene, go to Butters' House. Professor Chaos will greet you as you arrive. Follow him inside and up to his room. Shortly after, his dad will ground him and you in his room.
To get out, grab the blueprints on the desk. Then, grab the minion cape in the close right corner of the screen. Next, use Snap N Pops to get the rocket. Now, move the step stool to the bed to reach the Minion Aero Foil. Finally, move to the ladder to reach the hamster. Craft these components together to create the Flying Minion. Then, show this creation to Professor Chaos. Now, use Inspection Mode to examine the wires up by the door. Now, you can use the Haywire Buddy Power to short circuit door locks.
Before heading downstairs, go into Butters' parents' room to find a Haywire puzzle. Breach the safe to acquire the "Wrestling" Photo and The Ring of Engagement artifact.
Head downstairs to confront Butters' Dad.
He has the unique ability to "ground" your allies. This effectively renders them useless. Your ultimate ability will be replaced with a power to "unground" them. You will need to go around and use your turn to unfreeze your allies. In addition to having the power to "unground", your character is also immune to grounding. Start by ungrounding Professor Chaos. Then, move him to the other side of his dad. Next up, unground your other two allies.
The "grounding" attack is always telegraphed and covers a large area. If he is going to ground the next turn, don't bother ungrounding. Instead, get an attack in while you can. Focus your efforts on surrounding Butters' dad to avoid the full force of his grounding ability. This fight is actually pretty hard. Butters' dad also deals a good amount of damage. Be sure to come in with plenty of heals or healing abilities. It would also be a fine idea to avoid being hit. Defeat him to move on.
Next, meet up with Professor Chaos at Token's House. Use Haywire to fry the circuit and enter the Freedom Pals HQ. After the cutscene, the mission will end as you are inducted into the Freedom Pals. You will unlock combat buddies from the Freedom Pals, however those from Coon and Friends will be temporarily disabled until The Thin White Line.
Now head to your next mission, The Invitation.