The chain index, introduced by Alfred Marshall in 1887, calculates indices over multiple periods or regions by sequentially shifting the base period and multiplying the indices from each intermediate period. This method, praised by Irving Fisher in the early twentieth century, addresses issues with commodities changing over time and is expected to help narrow the gap between Laspeyres and Paasche indices. Chain indices, such as the chain Laspeyres and chain Paasche indices, can result in significant chain drift, especially with high-frequency data, leading to discrepancies between direct and chain indices. This drift occurs due to non-transitivity in standard indices and is exacerbated by product turnover and seasonal variations. While chain indices offer advantages in dealing with changing products, they also face theoretical and practical challenges, such as losing desirable properties like identity and monotonicity. Recent approaches like the GEKS method, which ensures transitivity by using the geometric mean of bilateral indices, aim to mitigate chain drift. However, when combined with rolling windows, even GEKS can exhibit chain drift. The use of chain indices requires careful consideration of their limitations and the specific context of their application.