In electric mixer, beat butter until smooth. Gradually add sugar and beat on high speed until light and fluffy. Add eggs, one at a time, blending well after each egg. Mix in orange peel and vanilla. Gradually stir in flour mixture until blended.
Press dough into a ball, then flatten into a round disk. Refrigerate until firm (about 2 hours).
Preheat oven to 350 degrees. Shape dough into 1-inch balls then roll on flat surface to form 3-inch logs. They should be about 1/2-inch thick. Place an inch apart on ungreased baking sheets.
Bake 14 minutes or until bottoms of cookies are golden brown. Tops will still be white and soft. Transfer to cooling rack.
Melt chocolate chips in double boiler. Sprinkle pecans on sheet of waxed paper or in a bowl. Dip one end of cookie in the melted chocolate, shaking off excess. Roll chocolate dipped end in pecans or use your fingers to sprinkle the pecans onto the chocolate. Place on waxed-paper sheets to rest until chocolate is set or refrigerate for about 5 minutes to quick-set the chocolate. Store in airtight container.