I just ran out of cocoa while making a cookie sheet cake. Had enough for the cake, but not for the frosting. Can I substitute chocolate chips?
You cannot substitute chocolate chips for cocoa alone, as they contain sugar and cocoa butter (fat), as well as cocoa solids—assuming you have quality chocolate chips that are true chocolate. The ratio of these ingredients will depend on the exact chips you have.
A reasonable approximation for the general case per What's Cooking America assuming you have semi-sweet chocolate chips is:
3 tablespoons unsweetened cocoa powder, 3 tablespoons sugar and 1 tablespoon butter, margarine or shortening for every 1 ounces of semi-sweet baking chocolate.
However, frosting is a specific application, and your recipe almost certainly has its technique based on powder, not melted chocolate. You would be better off looking for a recipe that starts with melted chocolate.
The easiest (and one of the best in my opinion) if you have cream on hand, and again assuming the chocolate chips are real chocolate, is to make a ganache; see Ina Gartner's recipe for reference.
The reverse question: Can I substitute cocoa for semisweet chocolate?
you can use the chips, just understand the frosting/topping will be different (sweeter and harder to blend)
melt the chips, add 2/3 to 3/4 of the ingredients from the original recipie, and add the rest to taste and consistancy (if it is too liquidy add sugar, if too thick add a liquid, if too sweet add fat etc) also note that the topping will thicken as is cools.