>I created a Silverlight project. Why is there no LinqToSql in the Add New Item dialog?

The Silverlight project is code that will run on the client (browser) side. You would not normally have any data access there but on the server side (You'll notice that it isn't just Linq-to-Sql - all other data options are likewise unavailable)

BTW, if you want to get a simple Silverlight app up and running try the 'Silverlight Business Application' project type - that will create both the Silverlight and Web site project for you and provide all the plumbing to link them together. Here's a good introductory video with an example using EF (you could use Linq-to-Sql but EF in probably a better choice these days) : http://www.silverlight.net/learn/videos/all/net-ria-services-intro/

You'll need the RIA services control toolkit etc. But beware : the video is a bit old and in a couple of cases classes have since been renamed and/or ended up in different namespaces or assemblies (for example the ActivityControl is now a BusyIndicator)