If you open the .aspx file and switch between design view and html view and
back it will prompt VS to check the controls and add any that are missing to
the designer file.
In VS2013-15 there is a Convert to Web Application command under the Project menu. Prior to VS2013 this option was available in the right-click context menu for as(c/p)x files. When this is done you should see that you now have a *.Designer.cs file available and your controls within the Design HTML will be available for your control.
PS: This should not be done in debug mode, as not everything is "recompiled" when debugging.
Some people have also reported success by (making a backup copy of your .designer.cs file and then) deleting the .designer.cs file. Re-create an empty file with the same name.
There are many comments to this answer that add tips on how best to re-create the designer.cs file.
Best Answer
You can use the chart controls in two ways:
Generating the Image from a Controller
By generating the chart and returning it as an image from an action (as Chatuman is referring to I think):
WebForms Style
This way you just include the chart in your .aspx views (just like with traditional web forms). For this you'll have to hook up the relevant bits in your web.config
You can't run code inside the DataPoint elements when building the chart, so to hook up your data you'll need a method in the View class. This works ok for me. Working this way makes the control render a URL to an image generated by the chart control http handler. In your deployment you'll need to provide a writable folder for it to cache the images.
* VS 2010 / .NET 4 Support *
To get this working in .NET 4 you need to change the chart references to version 4.0.0.0 with the appropriate public key token.
Also it seems that the chart control now generates urls to the current request path rather than the request route. For me this meant that all the chart requests resulted in 404 errors because
/{Controller}/ChartImg.axd
and equivalents were blocked by routes. To fix this I added extra IgnoreRoute calls that cover my usages - a more general solution would be better: