Ummm, you don't.
Just the name they use to identify the audio portion of the computer.
(Dell / Microsoft)
Chip and Chipset are slang terms for I.C.
The Chip, or Chipset (You can use either word), for sound; is the audio chipset.
If the audio chipset is mounted (Soldered) to a Printed Circuit Board, or also known as Card; it is a Soundcard.
Removable, therefore replaceable.
If the audio chipset is soldered directly to the motherboard; it is Integrated Audio, and not replaceable. (At least not easily)
The Dell Optiplex 360 Desktop PC uses Integrated Audio.
If indeed you do have a Soundcard installed, it would be mounted in a PCI slot on the motherboard, and it's outside bracket would be in an expansion slot, in the metal framework of the computer case.http://www.redplanettrading.com/ebay/cases/optiplex360/empty/smt/opti360-back-800.jpg
There are four such slots shown, in the empty Dell Optiplex 360 Small Mini, computer case shown above. They are at the bottom.
This is an example of a Soundcard,http://en.wikipedia.org/wiki/Audio_adapter
Perhaps you had no audio, went into Device Manager, and saw NO Device, listed.
This means Windoze lost the Drivers for the audio chipset.
Driver: Small piece of software that allows the Operating System to communicate with a device
Do not know what the O/S is.
The audio chipset is the device.
Post what version of Windows you are using.
In the meantime I'll use Windows Vista 32-bit as an example, as this is what the computer was supposed to come out with;
Dell Support > Optiplex 360 > Drivers & Downloads page,http://www.dell.com/support/drivers/us/en/19/Product/optiplex-360
The page automatically comes up with Windows Vista 32-bit, drivers; listed.
If you use a different O/S, click on the blue Down Arrow, to the right side of the box that has Microsoft Windows Vista 32-bit, in it.
(Under the blue Operating System subheading)
Here we see only 1 Audio file listed.
Click on the blue down arrow to the left of - Audio (1)
Click right on the blue name - Analog Devices - Driver
Now click on the blue - Download File - to the left of -
Update package for Microsoft Windows
Make sure there is a Green dot in the small circle, to the left of -
Download and save the file.
Then click on Continue in the blue oval.
[If there isn't a green dot, click in the empty circle ]
(Suggest install it yourself. Automatic features have a tendency to scr-ew up)
Green dot needs to be in small circle to the left of -
Click on Continue.
A small window will come up on the right -
Click on Save File
Another small window will come up on the left.
Allow the file to download all the way, then DOUBLE-click right on the file name.
(If somehow a Microsoft 'squawk box' comes up, ignore it.
"Warning this software does not have a digital certificate, ya-da, ya-da. Just click on OK. It is Okay.
At the bottom of the next 3 small windows, click on Next, Next, and Finish.
Close all windows,restart your computer if not asked to do so.
For additional questions please post in a Comment.