ChillingEffects.org is a website that collects and analyzes legal complaints about online activity. It is administrated by Electronic Frontier Foundation, which is a nonprofit organization located in San Francisco. As written on their website, ChillingEffects aims to support lawful online activity against the chill of unwarranted legal threats.
Google shows ChillingEffects if some of the websites were erased from the search result due to DMCA takedown notices.
So why does Google bother to do it? The reason should be clear — do you want unbiased search results based on Google's best-match algorithm, or do you want search results that are biased, that are somehow manipulated for unknown reasons? Since online search should be unbiased and that is what Google thinks, it explicitly lists ChillingEffects on its search results.