A good recipe for caramel chews is Martha Stewart's Classic Caramel Candies, which calls for heavy cream, sugar, light corn syrup, butter and vanilla. Another good recipe, Easy Four-Ingredient Soft Caramels, only uses butter, sugar, sweetened condensed milk and light corn syrup.
To make the Martha Stewart recipe, heat 2 cups of heavy cream, 2 1/4 cups of sugar, 6 tablespoons of unsalted butter and 1 1/4 cups of light corn syrup on high until the mixture boils and the sugar dissolves, and then continue cooking at medium-high for 15 minutes or until a candy thermometer reads 248 degrees Fahrenheit. Remove the saucepan from the heat, add 1/2 teaspoon of coarse salt and 1/2 teaspoon of pure vanilla extract, and pour the mixture into a greased and parchment-lined baking sheet. After eight to 24 hours, cut the caramel into squares, and wrap the individual pieces in waxed paper.
To make the four-ingredient recipe, melt 1 1/2 sticks of butter and 1/2 cup of sugar in a saucepan on medium heat, and then add 3 tablespoons of light corn syrup and 14 ounces of sweetened condensed milk. Bring the mixture to a boil, and reduce the temperature to a simmer until the caramel turns a dark golden color. Depending on the altitude, this can take from two to 10 minutes. Stir in any desired flavorings, and then pour the caramel into a foil-lined pan. Cut the caramel into squares once it cools completely.