It looks like the minimum amount of 1099 income to file schedule C is $400 - the reason for schedule C is computation of self employment taxes. If you made less than that amount you could probably just include it in Miscellaneous Income.
Although it may be news to you that you “have a business” (and most of the other people who get their first 1099-MISC); The IRS considers anything in box 7 of 1099-MISC to be self employment income. Enter the 1099-Misc income, at Other Common income / income from a 1099-MISC . TurboTax (TT) will complete Schedule C or C-EZ for you and allow you to deduct any expenses associated with this income. You'll also have to pay self employment tax (social security & Medicare) on any profits greater than $400. These types of payments are frequently done this way. Your "employer" is not the only one.
The IRS also considers undocumented cash income (no W-2 or 1099-MISC), for work performed, to be self employment income.