A redirect chain is as the name suggests, a chain of redirects. An issue a lot of websites suffers from. There are several caveats with redirect-chains and loops.
Loss of link value
If you know about Googles PageRank Formula, you will know that every page on a website, has an effect of 0.85 PageRank to realize the pages potential in the search engine result pages. The last 0.15 of the total value, is reserved for linking out to other webpages, both external as well as internal webpages. The last 0.15 or which can also be formatted as 15% is also the value, you will lose, when doing a 301 redirect.