Once you determine what determines the first rows, I like using this approach:

WITH cte AS (

SELECT TOP 1000

FROM TableName

ORDER BY EntryDate ASC)

DELETE FROM cte;

This gives the added benefit of being able to replace the DELETE with a SELECT so you can see the rows that are going to be deleted before you actually delete them. However, the fundamental question of the order remains. Since the ONLY way to guarantee the order is by using an ORDER BY clause, don't skip this step.