When a chain of 40 Pokémon is reached, the chances of finding a Shiny Pokémon greatly increase. The encounter rate becomes 1/200 when the chain has reached or surpassed 40 Pokémon. Before the chain reaches 40, the rate is still better than that of randomly finding a Shiny Pokémon in the wild. The encounter rate can be calculated by inputting the number of Pokémon chained, and then solving the problem.
Shiny Pokémon can appear if the chain is only at 1, though it is very rare. All Shiny Pokemon obtained through chaining are legit. However, some care must be taken if a person claims a Shiny Pokémon is chained, since they could always be lying.