Strategy to catch Chimecho. When it appears, paralyze it, use an attack that does a fixed amount of damage like Sonic Boom. Then throw a ball at it. ALternitively, if you have a Pokémon that knows it, use False Swipe.
Magneton with Thunder Wave and Sonic Boom
or
Sceptile/Ninjask with False Swipe.
Easy to catch really, I found two in a row.
Breed with a Ditto, found in the back of Fossil Maniac's House.