If you own your own business, you likely wear many hats. If you own a very small business (you're the only employee), you wear all the hats. You started a shoe-shine business; you're doing computer repair; you have a great website that sells Furbies. Congratulations.
Now you're looking for a traditional job. And on your resume, you list your title as CEO, likely because that is what you put on your business card. There is nothing wrong with considering yourself the CEO of your small business.
But should you put it on your resume?
When hiring managers see your resume and you are listed as CEO, they chuckle.
Were you appointed by your board of directors? What's that? You don't have a board of directors?
If you're company does not have a board of directors, the body to which a CEO typically reports, consider giving yourself a different title.
If you're a one-person shop and you give yourself the title of CEO, you can come across as being focused on prestige and how others perceive you, more than serving customers or achieving results.
How about just listing your title in plain english: Owner.