LINQ to SQL: Multiple joins ON multiple Columns. Is this possible?

Joining on multiple columns in Linq to SQL is a little different.

var query =
    from t1 in myTABLE1List // List<TABLE_1>
    join t2 in myTABLE1List
      on new { t1.ColumnA, t1.ColumnB } equals new { t2.ColumnA, t2.ColumnB }
    ...

You have to take advantage of anonymous types and compose a type for the multiple columns you wish to compare against.

This seems confusing at first but once you get acquainted with the way the SQL is composed from the expressions it will make a lot more sense, under the covers this will generate the type of join you are looking for.

EDIT Adding example for second join based on comment.

var query =
    from t1 in myTABLE1List // List<TABLE_1>
    join t2 in myTABLE1List
      on new { A = t1.ColumnA, B = t1.ColumnB } equals new { A = t2.ColumnA, B = t2.ColumnB }
    join t3 in myTABLE1List
      on new { A = t2.ColumnA, B =  t2.ColumnB } equals new { A = t3.ColumnA, B = t3.ColumnB }
    ...

In LINQ2SQL you seldom need to join explicitly when using inner joins.

If you have proper foreign key relationships in your database you will automatically get a relation in the LINQ designer (if not you can create a relation manually in the designer, although you should really have proper relations in your database)

Then you can just access related tables with the "dot-notation"

var q = from child in context.Childs
        where child.Parent.col2 == 4
        select new
        {
            childCol1 = child.col1,
            parentCol1 = child.Parent.col1,
        };

will generate the query

SELECT [t0].[col1] AS [childCol1], [t1].[col1] AS [parentCol1]
FROM [dbo].[Child] AS [t0]
INNER JOIN [dbo].[Parent] AS [t1] ON ([t1].[col1] = [t0].[col1]) AND ([t1].[col2] = [t0].[col2])
WHERE [t1].[col2] = @p0
-- @p0: Input Int (Size = -1; Prec = 0; Scale = 0) [4]
-- Context: SqlProvider(Sql2008) Model: AttributedMetaModel Build: 4.0.30319.1

In my opinion this is much more readable and lets you concentrate on your special conditions and not the actual mechanics of the join.

Edit
This is of course only applicable when you want to join in the line with our database model. If you want to join "outside the model" you need to resort to manual joins as in the answer from Quintin Robinson

U can also use :

var query =
    from t1 in myTABLE1List 
    join t2 in myTABLE1List
      on new { ColA=t1.ColumnA, ColB=t1.ColumnB } equals new { ColA=t2.ColumnA, ColB=t2.ColumnB }
    join t3 in myTABLE1List
      on new {ColC=t2.ColumnA, ColD=t2.ColumnB } equals new { ColC=t3.ColumnA, ColD=t3.ColumnB }