I lot of beekeepers in Melbourne, Australia say it works.
I put a banana in the top of a hive with chalk brood about a fortnight ago (yes it did seem silly - and looked silly on the hive mat), as well as feeding some suger water laced with Lemon Scented Tea Tree essential oil (about 0.1% - one part per thousand). Problem has eased a lot from seeing tens fo mummies each day to only one or two every other day. Last time I opened the hive I misted with a 1:1 sugar syrup with 0.1% oil again in a spray bottle so it would get on the frames in case there were spores left on the frames. The oil has been found effective in scientific testinig: see 'Control of chalkbrood disease with natural products' A report for the Rural Industries Research and Development Corporation by Dr Craig Davis and Wendy Ward (sorry there is no link, but the site wouldn't let me put the link in - google will find it with this info if you want to read it). Interestingly banana essence was not found to be effective, but the researchers said:There is some anecdotal evidence in Australia that banana fruit placed in hives is an effective control for chalkbrood. Our research has failed to find any inhibitory action of banana extract when it is incorporated into an in vitro culture system. Any beneficial effect that banana fruit placed within the hive might have in controlling or reducing the severity of chalkbrood would most probably arise from volatiles evolved by the fruit. It is not inconceivable that the fruit might evolve one or more volatile compounds that are inhibitory to the spore germination or mycelial growth of the causal fungus A. apis. Such fungistatic or fungitoxic/fungicidal volatiles might be the normal products of fruit metabolism or the products of microbial degradation of the fruit as it senesces. The banana fruit contains at least 200 individual volatile components (Palmer, 1971). Many more volatile compounds, including fermentation products, could arise from microbial action (Sureh and Ethiraj, 1991). Fermentation products (ethanol and acetaldehyde) have been shown to inhibit mould growth on oranges (Yuen et al., 1995).
My italians couldn't care less about the banana, and the syrup with essential oil really perks them up - they love it more than straight syrup. At present I am happy to leave the banana in there: it's doing no harm, and it is plausible that it could be helping with the gas it emits as it goes off