The table-toppers had plenty of chances in the first half and went ahead when a scramble was prodded over the line by Cook.
Chiltern’s wingers Donna Brown and Katie Street impressed on the flanks as the hosts added two more through Cook, one a bullet of a short corner and the other from open play.
Harpenden pulled one back near the end, with Cook and Brown voted players of the match.
In Division Three, the IIs were held to a 3-3 draw at Hertford IIIs.
The hosts went ahead in the first half and after several near misses, Chiltern levelled through Chelsea Wright.
Karen Murphy ran the length of the pitch only to be denied by a goal-line clearance, before it was 2-1 when Jackie Dadd found Wright and she set up Bethany Carlisle to score.
Hertford levelled with a dubious second goal, before Chiltern hit back to lead 3-2 as player of the match Carlisle was on target again.
Unfortunately an error in the Chiltern D resulted in a penalty corner right at the final whistle as captain Hayley Murphy was beaten by a late leveller.