Stucco clad framed chimneys are especially vulnerable to moisture intrusion. They are frequently improperly flashed at the roof line, improperly capped, and have only stucco cladding on the shoulders, which is insufficient for keeping excessive moisture out.
Remove all stucco, sheathing, wet insulation, and damaged framing
Replace all OSB or foam board with new 1/2" plywood
Install Tyvek with cap staples
Install 10mm Keene rain screen with cap staples
Install 7/8" Weep Screed
Install 7/8" expansion joint where required by code
Install self furring wire with vertical staples on framing members. All overlapping stucco wire not terminated on a framing member to be wire tied
Install Brown coat, scratch coat, and finish stucco coat completely
Install a piece of Flagstone on the chimney shoulder.