There is a similar question for 3.5 here:
Is there a built-in zip library in .NET 3.5?
that speculated that 4.0 would have it, but I can\'t find any info abo
Not for 4.0, but a ZipArchive
class is being considered for the next version. You can find details about this on the BCL Team blog.
Edit: Otherwise, assuming that it's still available, and depending on your definition of built in (at least it comes/came with Visual Studio), you might be able to use the J# classes to zip files as described in this article: Using the Zip Classes in the J# Class Libraries to Compress Files and Data with C#
Edit2: Though note the comments below, that the J# option is probably not the right option except in certain unusual circumstances.
You may have already moved along, but ZiP API is added in .NET 4.5
http://msdn.microsoft.com/en-us/library/system.io.compression.ziparchive.aspx
go nuts.
Most easiest to deal with, is with sample code here.
You need to add a new assembly just to find he Zip archive.
Working with Zip files in .NET 4.5
Take a look at the System.IO.Packaging namespace, which contains support for ZIP files, but not all of the features of ZIP files.
Still, it might be enough for your needs.