Chiarelli's success in Boston was entirely down to him having the opportunity to sign, and then signing, a dominant #1 defenseman. That's an exceedingly rare occurrence in today's NHL. The other key cogs of the Cup run (Bergeron, Krejci, Lucic, Thomas) were acquired prior to his time in Boston. Beyond that, he essentially just needed to find the supporting cast.
While Edmonton's got the key cogs offensively, they've got next to nothing defensively if Nurse doesn't become a true #1. So I'm not sure how good of a fit he is there. The good news for Edmonton fans re: Chiarelli is that he's not afraid to do something bold (see: Kessel and Seguin trades). That's exactly what the need. Two of Hall, Eberle, and RNH need to be moved for defensive help. I'd make Don Maloney turn down RNH for OEL.