I think it would be easier to do it with the ions involved,
NO3- is the nitrate ion, since the overall charge of the anion is -1, you don't need to worry about the O's and the N's as they are unimportant. So since there are three nitrate anions, their total oxidation number is -1 x 3 = -3 so it makes sense that the O.N of the chromium is....