This paper proposes an interpolation based progressive algebraic Chase decoding (PACD) algorithm for Reed-Solomon (RS) codes. Based on the received information, 2η (η > 0) interpolation test-vectors are constructed. They are ordered using a reliability function, assessing their potential of yielding the intended message. The decoding is performed progressively granting priority to decode the test-vectors that are more likely to yield the intended message, and it will be terminated once the intended message is found. In the proposal, the decoding of a later test-vector utilizes the interpolation information that is generated during the decoding of the earlier ones. It results in the binary tree that represents the evolution of the interpolated polynomial sets growing in a depth-first-search manner. The PACD algorithm has the advantage of adapting its decoding computation to the channel condition, leveraging the average decoding complexity. This channel dependent feature will be validated by our simulation results which show that the PACD algorithm is less complex than various interpolation based algebraic decoding algorithms. We will also demonstrate that it can achieve a high RS decoding performance.