I wouldn't. Too easy for someone to steal it, and if it's good, they WILL steal it. I have an online friend who published part of a story on a writing board. Someone stole it, finished it, published it, and had the nerve to brag about it. This person was an idiot, though. They didn't even change a thing, put her text verbatim into their story, so they were easily caught. Stupid.
But most plagiarizers are not that stupid. Say you put an entire chapter here, they jazz it up, send it off, get a book deal out of it. Your story is gone, and you have to start over.