I heard in this question: http://pokemondb.net/pokebase/170572/will-your-chain-reset-when-you-find-a-shiny that the chain is still continuing after you catch your desired shiny Pokemon. And I tested this myself, chaining a shiny Jigglypuff. After I caught my shiny (chain of 40), the grass continued to shake. Does this mean that the chain continued? If so, are the odds still as high as they were before I found my shiny?
The grass will still be shaking after catching a shiny, however the chances of finding a shiny will reset.
Hope I helped. :)