Facebook doesn’t allow users to change the “pop” sound alert heard on receiving of a new message, but if you want to customize the sound alert take a look at FaceSounds.
FaceSounds is a Google Chrome extension that gives you the ability to set different sounds to Facebook chat.
After installing the extension, you will find a new icon next to Facebook chat bar. Clicking on it will open the FaceSounds sounds list.
From here you can preview and set any sound you like. If you want, you can also disable the sound alert by selecting the last option - Mute (No Sound) – in the list.
FaceSounds does not provide you with an option to select a sound from you computer, but that’s because of Chrome restrictions.
Note: If you have Secure browsing (https) enabled, you may get a warning as below.
Download: FaceSounds for Google Chrome