Genome editing using sequence-specific nucleases (SSNs) offers an alternative approach to conventional genetic engineering and an opportunity to extend the benefits of genetic engineering in agriculture. Currently available SSN platforms, such as zinc finger nucleases (ZFNs), transcription activator-like effector nucleases (TALENs), and CRISPR/Cas (clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR-Associated systems (Cas)) have been used in a range of plant species for targeted mutagenesis via nonhomologous end joining (NHEJ) are just beginning to be explored in crops such as potato (Solanum tuberosum Group Tuberosum L.). In this study, CRISPR/Cas reagents expressing one of two single-guide RNA (sgRNA) targeting the potato ACETOLACTATE SYNTHASE1 (StALS1) gene were tested for inducing targeted mutations in callus and stable events of diploid and tetraploid potato using Agrobacterium-mediated transformation with either a conventional T-DNA or a modified geminivirus T-DNA. The percentage of primary events with targeted mutations ranged from 3-60% per transformation and from 0-29% above an expected threshold based on the number of ALS alleles. Primary events with targeted mutation frequencies above the expected threshold were used for mutation cloning and inheritance studies using clonal propagation and crosses or selfing. Four of the nine primary events used for mutation cloning had more than one mutation type, and eight primary events contained targeted mutations that were maintained across clonal generations. Somatic mutations were most evident in the diploid background with three of the four primary events having more than two mutation types at a single ALS locus. Conversely, in the tetraploid background, four of the five candidates carried only one mutation type. Single targeted mutations were inherited through the germline of both diploid and tetraploid primary events with transmission percentages ranging from 87-100%. This demonstration of CRISPR/Cas in potato extends the range of plant species modified using CRISPR/Cas and provides a framework for future studies.