I would either say that he was drafted to the army, or he moved away. How would you send off his character? (or maybe not remove him at all, and incoprperate him into the later seasons)

I can actually kind of see why they removed Chuck from the show. For one, he had barely any screentime in most of the episodes he did appear in ("Richie Moves Out" may be the only exception). He had no less than three actors portraying him. One for the pilot, one for Season 1, and yet another for Season 2. When the third actor quit, I guess they decided it just wasn't worth it anymore. Plus, Fonzie was already playing a big brother role for Richie, so Chuck felt kind of redundant.

Anyway, I would have just written him off as moving away for college.

Garry Marshall on Chuck's disappearance:

https://youtu.be/QQoOdmd77Hk

They could have just made him an offscreen character.

The third actor (Randolph Roberts) wasn't the one that quit. That was the second Chuck (Gavin O'Heirly). Gavin wanted to go back to school, so he asked Garry Marshall to be let out of his contract. They fired Randolph, probably as the mission to remove Chuck from the series' canon.

They could have just made him an offscreen character.

This is what I would have done.

But many shows simply do what Garry Marshall did.

The third actor (Randolph Roberts) wasn't the one that quit. That was the second Chuck (Gavin O'Heirly). Gavin wanted to go back to school, so he asked Garry Marshall to be let out of his contract. They fired Randolph, probably as the mission to remove Chuck from the series' canon.

I wonder why Gavan O'Herlihy quit in the first place. Maybe he felt he wasn't getting enough? After all, in Season 1, Chuck got maybe 5 minutes of screen time, if that, in all the episodes he appeared in put together.