A veteran pharmacist, who worked at CVS Caremark Corp. until last year, filed a civil lawsuit against his former employer this week, alleging he was wrongfully discharged—in part, because he complained to management that staff cutbacks were contributing to increased pressure on pharmacists, causing prescribing errors.

The lawsuit, filed Wednesday at a U.S. District Court in Harrisburg, Pa., is one of the latest developments reflecting the growing tension between chain pharmacists and their employers, as drugstores increase...