The Greenway mentioned above doesn't really touch the Dee except at the very end so I doubt it's the path meant by the OP. The Dee does however have a river path (not new though) and is easily accessed from the above Greenway, leave Greenway on canal heading south (brown route bike path signs) and after crossing spiral cobbled bridge leave path at next bridge opposite Telford's Warehouse pub, turn right and down to T junction and path starts virtually opposite in a small park.
Start is Mickle Trafford as in Paul's post and ends at Dee crossing to access NCN5
Route:-
http://bikeroutetoaster.com/Course.aspx?course=583402
The canal link may be busy and the spiral cobbled bridge is deadly in ballet type road shoes, slippy even in SPD's!
The wind is always againsterly on the river (or Greenway) but both are easy cycling once clear of town and strollers.
The only new Dee path I can think of could be the Burton Marshes Greenway (NCN568) but that starts at the Dee where Greenway ends - well near enough and that route runs up the Wirral.
Best spiel here:-
http://www.chestercyclecity.org/?p=859