Delete item using CLient Object Model

"Client" in the namespace.  For example, in the server object model you have:
Microsoft.SharePoint.SPSite
Microsoft.SharePoint.SPWeb
Microsoft.SharePoint.SPList

In the client object model you have:
Microsoft.SharePoint.Client.Site
Microsoft.SharePoint.Client.Web
Microsoft.SharePoint.Client.List


NameSpace:


Microsoft.SharePoint.Client.dll
Microsoft.SharePoint.Client.Runtime.dll


Example Code:

ClientContext context = new ClientContext("http://peakfinders.com");

Web web = context.Web;

List list = web.Lists.GetByTitle("yourlistname");
ListItemCollection listItems = list.GetItems(new CamlQuery() { ViewXml = "<View/>" });
context.Load(listItems);
context.ExecuteQuery();

listItems[listItems.Count - 1].DeleteObject();
context.ExecuteQuery();