Generalized integrated interleaved (GII) codes are essential to next-generation digital communication and storage systems since they can achieve very high decoding throughput with low complexity. Only hard-decision GII decoding has been considered in previous work. To further improve the error-correcting capability, soft-decision decoding algorithms utilizing the channel probability information need to be developed. The decoding of GII codes constructed based on BCH codes consists of multiple rounds of BCH decoding. Among existing soft-decision decoding algorithms of BCH codes, the Chase algorithm that carries out decoding trials on multiple test vectors can achieve a better trade-off on the coding gain and complexity. Although one-pass Chase algorithms can derive the error-locator polynomials for all the test vectors in one run, the exhaustive Chien search is carried out previously on each error-locator polynomial to decide which one is correct and it leads to long latency. For the first time, this paper proposes an efficient soft-decision GII decoding algorithm. Different methods of incorporating the Chase process into the GII scheme are analyzed and compared to identify the best GII Chase decoding algorithm. Besides, a new error-locator polynomial selection scheme is developed to avoid carrying out the Chien search on each error-locator polynomial by pre-flipping a bit in the received word. Accordingly, the error-locator polynomial can be selected by testing whether it consists of a pre-determined factor. The latency is further reduced by pre-computing short remainder polynomials in our second proposed scheme. In addition, formulas have been developed to estimate the error-correcting performance of the proposed designs. This paper also develops low-complexity hardware architectures to implement the proposed GII-BCH Chase decoders. For an example GII-BCH code with 8 sub-codewords of 4095 bits over $GF(2^{12})$ , the proposed GII-BCH Chase decoder can achieve significant coding gain over hard-decision decoder with negligible silicon area overhead. Besides, our proposed designs can reduce the worst-case latency of GII-BCH Chase nested decoding rounds by 54%-80%.