The agency is thought to have triumphed in a pitch against Doner Cardwell Hawkins, which has worked with the company in the past, and one unnamed agency.
The shops were briefed to come up with an above-the-line strategy for the storage company over the next three to five years.
The pitch was overseen by Rob Strachan, the company's marketing director, who joined earlier this year. CHI has ties to the company via its relationship with David Ross, Big Yellow's deputy chairman and the co-founder of The Carphone Warehouse, the agency's founding client.
Big Yellow's most recent high-profile activity was sponsorship idents, created by Adlab, around ITV's London's Hottest Properties in 2004.
Strachan said the process had not been concluded. Clemmow Hornby Inge was unavailable for comment.
This article was first published on Campaign