How can I disable Skype chat beeps and audio?

I do a lot of business via Skype and often have a chat window open with my partner while we’re on the line with a client. We have a backchannel conversation going on so we can ensure we’re in agreement on terms, schedules, etc, but what drives me crazy is that each time I get a chat message there’s a small “bloop” sound. Can I turn this Skype audio notification off?

There are a couple of ways you can sidestep this, the most obvious of which is to actually connect via a different instant messenger service with your partner, but there’s also an easy way to tweak Skype to stop pushing out those annoying audio notifications.
I’m with you too. They drive me crazy, and for me it comes up while recording episodes of my two weekly podcast programs Boulder Open Podcast [iTunes] or Three Insight [iTunes]: while we’re chatting we’ll also IM each other time checks, reminders of other topics, etc. Audio notification is not appreciated!
If you have external speakers, you can configure your Mac or PC to use the built-in speaker for notifications, while the audio out from the Skype session itself comes out the external speakers, but that too is a bit of tricky work and might mean that your music, streaming video, etc, doesn’t work as you expect either.
Instead, turns out that Skype offers all sorts of ways you can customize the per-event notifications, whether it’s when you first connect to Skype, when someone wants to send you a file, when a friend connects, or – what we want – when you receive a message.
First step is to launch Skype then go to your Preferences. I’ll show you these steps on the Mac, but it should be identical on the PC once you’re in the Preferences/Settings area:

That’s not what we want. Click on “Notifications”:
skype chat message audio 2

Now we can see just how many different notifications are available in Skype and tweak them as desired. Click on the Event pop-up and you’ll see that there are quite a few options:
skype chat message audio 3

To turn off the audio notification sound when the event “message received” occurs, choose that particular event, then uncheck the box adjacent to the “Play sound” menu. You can also choose to have the Skype app icon in the toolbar indicate an event has transpired too, if you’re so inclined. I hate that, actually, so I always disable it. In fact, here’s an example of how I set it so that when friends logged in to Skype I wouldn’t get any notification:
skype chat message audio 4

Go through this event by event and you’ll find that you and your partner will be able to have that backchannel discussion while on the line with your client, and all they’ll hear is the occasional clickety-clack of keys on the keyboard!