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This is a fairly quick quest if you know what to do. If you talk to Follows-Chalk about the local wildlife, he should mention that the local bighorner herds are all riled up. This is bad for everyone, since the tribes will either face a food shortage or have to kill the angry bighorners and destroy the local herd. He figures that a calf has gone missing, and believes that you can take care of things. You'll need to have three banana yuccas for this, but you can probably grab a few along the way. You can get these banana yuccas by looking for the tall stalks along the sides of the roads throughout Zion.
Ideally, he wants you to avoid killing any of the bighorners, since that will just make things harder on them. It's probably worth a shot, at least. You'll get more of a reward if you can do it, and it's not too hard. If you choose to do this, you will probably want to ditch Follows-Chalk at camp, since he has a chance of messing things up for you. Bighorners killed by your companion will count toward your count, even if you never fire a shot. If they're set to fire at will, then you'll probably lose the optional objective. Don't worry, especially if you still have Follows-Chalk. You can just fast travel back and find him at the camp afterward.
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Finding the Bighorner Calf
In order to help, you'll need to walk up into their hunting grounds. Go to the Dead Horses Camp and look for a slope just past the tents. You can climb up this slope to enter the mountains. Just keep following this until you make it to a natural rock bridge. You'll pass a mother right before you cross it. Just note that this is where you're taking the calf to. It'll make the next part easier to know where you're coming back to. The mother also shouldn't be hostile, so she's easy to spot.
As a rule, even though the bighorners are hostile, they won't attack unless you get really close to them. They'll snort if you agitate them. That snort is your warning to quickly get out of the circle. If you move quickly and skirt around them on the edges, you shouldn't actually have too many problems. Note that the babies won't attack you, so feel free to skirt close to them to avoid their parents. In a few spots, this is really the only way to even get through.
Cross the first bridge and then the second, then quickly jump up the slopes and stick to the wall to go around the bighorner here. Keep an eye out for banana yucca fruits along the way too, since you shouldn't turn those down. Move across the last bridge and shoot the gap between the two bighorners to enter the small canyon in back. Go all the way back down the canyon and interact with the lost calf to feed it a banana yucca. After a few seconds, it will run after you.
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Returning the Calf Safely
Save now! I can not stress that enough. The pathfinding is flaky and it's possible that a bighorner could also just wander into a chokepoint and make this impossible to complete optimally. The calf will stop right before the first bridge regardless of how fast you go, and you'll need another banana to get it moving again, so be ready to turn back at that point. At the end of the second bridge, just cut the corner and drop off the side to avoid the bighorner. Wait for the calf to catch up across the gap and then feed it again to take it across the final bridge and reunite it with its mother at the start.
Just wait for it to catch up and then approach her, and you'll get the option to return the calf. Once you do this, the bighorners will become neutral. Travel back and report your success to Follows-Chalk. He should just be waiting at the campfire back at the camp. Naturally, you'll receive his heartfelt thanks. You'll receive the more tangible benefits of some experience, a war club and a free .45 pistol and 10 HP rounds for it. If you killed a bighorner, then you will only get the war club.
This will wrap up the quest for you. Remember to pick up your companion again and get back to your adventures in Zion Park.
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All information and screenshots from Fallout:New Vegas DLC - Honest Hearts