Many clients hire a personal chef because they don't have the time or desire to prepare meals themselves. Personal chefs are also popular with people with specific dietary needs and restrictions and those looking to broaden their culinary horizons or eat healthier. For example, both you and a competing personal chef may target athletes to be your marketing segment, but each of you can offer them different services. Just find your niche and hold on to it. A good way to define your target market is to have a compilation of all the recipes you've perfected and the environments that appeal to those foods.
If you're good at preparing healthy meals, then your target market should be people with health problems or on strict diets. But, if your specialty is international cuisine, you might consider targeting couples looking for a private romantic dinner or the elderly people mentioned above. Other people who could benefit from having a private chef include people with special dietary needs, older people, couples who want a private dinner, and just about anyone who wants to be exposed to new foods and flavors.