!rant
Is there any way that I can trigger a desktop application through a JavaScript on Chrome?

Yes.. you can, similar to notifications you get or you can take the approach and hack something together where there is this layer in Windows where programs interact you can run machine code in it to do anything you want ... And you can access that with JavaScript

Eh everyone! Quiet! Stop right there.
There is a new kind of browser add-ons called WebExtensions which work on Firefox and Chrome. Basically Web Apps on steroids. This technology has a standard called "Native messaging". Have fun!

you could use a url scheme that the application has registered itself as a handler for.

@darksideplease your answer is really helpful!
Others, thank you for all your help.