They're talking about mountain climbing. Mountain climbers chain each other. So if one falls, they all fall.
8 seconds sound clip from the Race for Your Life, Charlie Brown movie soundboard.
You can hear this line at 00:58:06.050 in the DVD version of the movie.
Quote context
[...]
- Okay. If that's the way they want to play, we'll sleep outside. Come on. Let's make camp.
- Put on chains? Being lost up here in the middle of nowhere isn't enough. We gotta wear chains too!
- Good grief, Sally. Don't you know anything?
- Okay, troops. Time for chow. Let's go find the guys. Maybe they got breakfast started.
- Hey. Reminds me of Christmas. Maybe we should pick out a Christmas tree.
- Great. Let's get a big one painted red.
- No. I want one of the short, fat ones.
- From up here, we get a good view. Let's pick out our trees.
- Hey! It's Chuck and his gang. Chuck, what's going on?
[...]