In this paper we propose a method that can address a novel task, audio effect (AFX) chain estimation and dry signal recovery. AFXs are indispensable in modern sound design workflows. Sound engineers often cascade different AFXs (as an AFX chain) to achieve their desired soundscapes. Given a multi-AFX-applied solo instrument performance (wet signal), our method can automatically estimate the applied AFX chain and recover its unprocessed dry signal, while previous research only addresses one of them. The estimated chain is useful for novice engineers in learning practical usages of AFXs, and the recovered signal can be reused with a different AFX chain. To solve this task, we first develop a deep neural network model that estimates the last-applied AFX and undoes its AFX at a time. We then iteratively apply the same model to estimate the AFX chain and eventually recover the dry signal from the wet signal. Our experiments on guitar phrase recordings with various AFX chains demonstrate the validity of our method for both the AFX-chain estimation and dry signal recovery. We also confirm that the input wet signal can be reproduced by applying the estimated AFX chain to the recovered dry signal.