You can find recipes for homemade mayonnaise in the Joy of Cooking. I wouldn't do it myself, for two reasons: too much work, and the raw eggs could have salmonella.

In the U.s., at least, it is important to distinguish between real mayonnaise and the substitute stuff, such as Miracle Whip. Miracle Whip has a slimy texture and sharp taste. Hatum duts!

Delicious chicken breasts (seduction dinner #46)

Mix sauce: ahead of time, whisk together a dollop of mayonnaise, an equal amount of yogurt, and a teaspoon or so of dried tarragon. (Amounts depend on how many people you are feeding.) Grind in a modest amount of black pepper. Place in the refrigerator to blend.

Cook chicken: flatten chicken breast meat between sheets of wax papr, using a hammer, beer bottle, or banjo. Saute the chicken breast in butter or olive oil till pinkness is gone. Let rest (absorb its own juices) for a few minutes and serve with the sauce, along with good bread and a fresh vegetable.
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What background music do you think would go well with this?