A Bing Community thread talks about Bing's crawlers and indexers ability in following chains of redirects. A redirect chain is when you have two or more URLs that are being redirects to another URL. For example, if I have domain.com/pageA redirect to domain.com/pageB and then from domain.com/pageB to domain.com/pageC - that is a redirect chain.
Search engines typically crawl them fine, if they are done using 301 redirects. But it takes them a longer time to figure multiple redirects in a chain of redirects. I believe most search engines can handle them, but your job as an SEO is to make sure to limit the number of redirects to one or so, so there is not a long chain.
Brett Yount from Bing even said they do not like redirect chains. In the Bing Community, he said:
While we do not like redirect chains, we are able to follow them. But if you have a 302 redirect in the chain--even if there is a 301 after it--expect that the page may not get all of the potential rank or may not get indexed at all.
Forum discussion at Bing Community.