The answer is, without question, yes. However, all companies have one. In companies that are too small to invest in a full-time CMO, the CEO is the defacto CMO whether he or she sees it that way or not.
Recently, Wrigley (the gum company) announced they were eliminating the separate CMO position. The reasons are not clear as the standard “we appreciate the contribution…” is what was publicly stated. However, they do not appear to be searching for a new CMO. Possibly because the gum category is in decline and they are looking to cut costs.
Whether this is a good idea or not, I cannot say, but I do note they also stated that “marketing would be overseen by Casey Keller, Wrigley North America president…”
All companies have a CMO, whether he/she is full-time or part-time, is not the point. Whether they have the responsibility and authority to truly oversee “Marketing” is the real issue.