Customs in Chile and Argentina?

Customs duties in both Chile and Argentina are high, and if you have multiple nice watches, there is a reasonable chance that customs agents in both places will suspect you are trying to bring watches in to sell them or as gifts. Also, when I was in Buenos Aires, a member of our party had a valuable possession snatched out of his hand by a thief who made off quickly on a bicycle. Personally, I wouldn't take nice watches on a trip like that. Just too many ways for things to go wrong with all the traveling and touring.

I'm with Dan S way too many things that can go wrong. I returned a couple weeks ago from the U.K. and was going to bring some of my watches, but based on some of the threads I've read, I decided to just bring my Speedy. (Not a knock against the U.K. Just too many things can go wrong when traveling anywhere with multiple watches)

Buenos Aires isn’t very safe these days. I wouldn’t wear anything expensive.

After initially not traveling with any of my watches over ~$2-3k, I subsequently had a change of mind and decided, as long as they are insured, and as long they are not vintage / hard to replace, and as long as I don't make myself too much more of a target, I may as well enjoy them whenever I'm inclined, including while traveling internationally. I know other people will feel strongly / differently about that, and that's ok.

That might be too tangential to your original question re: customs, but for that, I find it hard to believe (other than that fiasco in Switzerland a few years ago) that you'd get hassled for having 2-3 watches on you. Worst case, perhaps just keep digital copies of your original purchase receipts handy to show customs officials if need be...