Generally, the chances for any OOS applicant to UNC-CH are somewhat problematic due to the highly competitive nature of OOS applications there: UNC-CH admits OOS applicants in numbers that are calculated not to exceed 18% of an entering freshman class. See “Undergraduate Admissions” on Page 2, here: http://www.admissions.unc.edu/files/2013/09/Admissions__Policy.pdf. As a further example of the difficulty for OOS students to be admitted to UNC-CH, the entering Class of 2021 had a 14% acceptance rate for OOS applicants: http://admissions.unc.edu/apply/class-profile-2/.
If you look at the UNC-CH Common Data Set, under Part C7 it states that standardized test scores, application essay(s), letter(s) of recommendation, and the rigor of your high school record are “very important” academic factors considered for freshman admission, whereas GPA and class rank are “important” academic factors considered for freshman admission. Extracurricular activities, talent, and character/personal qualities are considered as “very important” non-academic factors.
Further, Part C9 of the Common Data Set for UNC-CH gives the median 50% for both SAT and ACT scores, as well as the percentage of the entering first-year class falling within certain ranges of SAT and ACT scores; Part C11 gives the percentage of entering first-year students falling within a range of unweighted GPA on a 4.0 scale, and Part C12 gives the average high school GPA of first-year applicants.
Having stated all of the above, your ACT score and GPA are, IMO, a bit low to make you very competitive for admission as an unhooked OOS applicant. If you have good essays and letters of recommendation, that will help.
By way of comparison, our OOS high school usually has 8-10 students who apply, and 1-2 students who are admitted, each year to UNC-CH; and, with the exception of legacy students, our admitted students have ACT scores of 33+ and weighted GPAs of 4.4+. These successful applicants also were involved in extracurricular activities that showed commitment over time (no “drive-by” ECs), and demonstrated leadership in the school as well as their ECs. Other kids in our city who I know were admitted to UNC-CH recently also had similar academic statistics and non-academic characteristics; and all of these kids were “unhooked” in admissions parlance (i.e., not a recruited D-1 athlete, or a URM, first-generation college student, etc.).
Also, the cut-ff for top 10% in a class of 538 would be 53.8.