I had the same thing happen at my lake house when I first bought it. My chimney had a concrete top that failed. I bought it in November 2012 and promptly left for a vacation in Jamaica only to receive a phone call saying that my living room has a huge puddle of water...

The solution was the same: first tarp and then me and my dad replaced the one inch concrete top on chimney with a 5 inch metal rebar reinforced chimney top. That thing is forever...