DAO Example - I dont think you can do this with the ALTER TABLE Statement...

Code:
Sub ZeroLengthField()
    Dim dbs As Database, tdf As TableDef, fld As Field

    ' Return reference to current database.
    Set dbs = CurrentDb
    ' Return reference to Employees table.
    Set tdf = dbs.TableDefs!Employees
    ' Create new field in Employees table.
    Set fld = tdf.CreateField("SpouseName", dbText, 15)
    ' Allow zero-length strings in field.
    fld.AllowZeroLength = True
    ' Append Field object.
    tdf.fields.Append fld
    Set dbs = Nothing
End Sub