We use a technique due to Keleti to provide an example of a set in F_3[[t]] of Hausdorff dimension 1 that does not contain any 3-term arithmetic progressions. This contrasts with a 2016 result of Ellenberg and Gijswijt, which states that every subset of (Z/3Z)^n with at least 2.756^n elements must contain a 3-term arithmetic progression.