Facebook will by default play a sound whenever you receive a chat message: this will of course only be noticeable if you have speakers on your computer, and if the sound volume is turned up enough. But these chat sounds are redundant in the sense that you do get a visual notification (as shown on the screenshot below) that a new message has arrived through Facebook Chat even if you didn't have an active conversation going with another Facebook user either inside the main window or in a chat window in the background (how to open Facebook Chat in a new window). But like most other settings, Facebook lets you turn off and disable chat sounds altogether, as you'll learn in this tutorial.
Follow these steps to mute the new chat sound in Facebook:
Note that turning off chat sounds is a "persistent setting" - in other words, once you close the web browser window and log back in later on, even from another browser and different computer, Facebook will remember this option for your profile, and you do not need to disable chat sounds every time.