Realize that you may have two records where Max(Amount) is exactly the same. What do you want to do then? If you don't care then try this. Done in Access 97 but should work anywhere for SQL. This is just one way of getting to the answer, there may be more.

Code:
SELECT TOP 1 test.Field1, Max(test.Amount) AS MaxOfAmount
FROM test
GROUP BY test.Field1
You can't return "*" records because of the aggregate basis of the query. You must use every field name. But this will return the record where the Top 1(st) is the Max of Amount. If you have two records with the same amount that is the hightest, then the record returned will be the Sorted item of the fields left to right.

Hope this helps...