Code:
SELECT Table1.*
, Table2.some_other_colulmn
FROM Table1
INNER
JOIN ( SELECT linkfield
, MIN(datefield) AS min_date
FROM Table2
GROUP
BY linkfield ) AS m
ON m.linkfield = Table1.linkfield
INNER
JOIN Table2
ON Table2.linkfield = m.linkfield
AND Table2.datefield = m.min_date
notice that the SELECT clause contains "some other field" from Table2
if it was really the lowest datefield that you wanted, the query would be a lot simpler
usually, this type of situation wants to have some other column value on the row that has the lowest datefield for each group