The agency took the account from incumbent Doner Cardwell Hawkins, which has worked with the firm since 2002, and one unnamed agency.
The pitch was overseen by Rob Strachan, the company's marketing director. The competing agencies were challenged to come up with an above-the-line strategy for the storage company over the next three to five years.
David Ross, a non-executive director of Big Yellow, is a co-founder of Carphone Warehouse, which has a long-standing relationship with CHI.
Neither Big Yellow nor Clemmow Hornby Inge were available for comment.
Big Yellow Self Storage, which owns and operates 60 sites around the UK, is a fully listed FTSE 250 company.
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