It is highly unlikely that the Downtown YWCA's recipe for chocolate-chip cookies will ever be revealed. But that doesn't stop people from asking. Or from trying to reproduce it.

The popularity of the cookies has fended off competition from Famous Amos and the Famous Amos knock-off called The Famous.

But a cooking teacher in Arlington took up the chocolate-chip cookie challenge two years ago when the Y re-buffed her request for the recipe. Caro Finkelstein's two-year struggle to recreate the Y's chocolate-chip cookie is all her husband's fault, she explained recently.

"He came home one day raving about the Y cookies so I called and asked for the recipe. The woman at the Y was incensed that I had the nerve to ask for it. So I started working on the recipe and set out to duplicate or better it.

"I noticed it contained angel-flake coconut and used more baking soda than a regular Toll House cookie. I experimented for two years and I finally got a cookie that tasted almost like it." At one point she even contemplated having the Y cookie analyzed by a lab.

"I brought in both cookies for my students to try and they preferred mine."

That might not be considered a fair test, but among 12 tasters at The Washington Post last week, Finkelstein's cookie did as well as the Y's. Opinion over which was better was split right down the middle.

Finkelstein, who teaches international cooking for the Arlington County Adult Education program, was happy to share her recipe. CAROL FINKELSTEIN'S CHOCOLATE CHIP COOKIES (Makes 12) 1 1/3 cups unsifted hardwheat flour or all-purpose flour 1 teaspoon baking soda 1/4 teaspoon salt 4 tablespoons butter 1/4 cup vegetable shortening 1/2 cup granulated sugar 1/4 cup dark brown sugar 1 teaspoon pure vanilla extract 1 large egg 1/2 cup coarsely chopped walnuts 1/4 cup angel-flake coconut 1/4 cup chocolate chips

Mix together flour, soda and salt Cream together butter, shortening and sugars. Beat in the egg and vanilla. Blend flour into creamed mixture. Mix in walnuts, coconut and chips. Divide dough into 12 equal parts. Flatten each part into a 3 1/2-inch round. Place on greased baking sheet and bake on lowest shelf of oven at 375 degrees for 15 minutes. Even if the cookies look underbaked, Take them out.