Potato (Solanum tuberosum L.) breeders are interested in developing chipping cultivars that can be stored at cold temperatures to reduce storage losses and increase profitability for potato producers. Commercial cultivars accumulate reducing sugars during cold storage, resulting in unacceptably dark chips when processed. In this study, we have identified diploid wild Solanum species accessions that are resistant to cold‐induced sweetening at very low storage temperatures (2°C). Selected accessions were crossed as males to haploids (2n = 2x) of S. tuberosum to produce adapted hybrids, some of which produce acceptable chips following 3 mo of storage at 2°C. Reconditioning for 6 d at 20 to 22°C increased the number of clones with acceptable chip scores by threefold. The best wild species parents were S. raphanifolium 296126, 310998, and 210048. While parental chip scores help to predict offspring performance, progeny testing is important to identify the best cross combinations. The best hybrids have been introgressed into diploid and tetraploid breeding clones. These hybrids produce good tuber type and low levels of reducing sugars under extremely low storage temperatures.