SQL set allowed values for a column

alter table ExampleTable
    add (new_column varchar(20) default 'value1',
         constraint ckExampleTable check (new_column in ('value1', 'value2', 'value3')));

You should actually do this as two different statements:

ALTER TABLE test
    ADD new_column VARCHAR(20) DEFAULT 'value1'

ALTER TABLE test
    ADD CONSTRAINT CK_exampleTable_newColumn CHECK (new_column IN ('value1','value2','value3'))