Context. [¹³C II] observations in several Galactic sources show that the fine-structure [¹²C II] emission is often optically thick (the optical depths around 1 to a few). Aims. Our goal was to test whether this also affects the [¹²C II] emission from nearby galaxies like the Large Magellanic Cloud (LMC). Methods. We observed three star-forming regions in the LMC with upGREAT on board SOFIA at the frequency of the [C II] line. The 4 GHz bandwidth covers all three hyperfine lines of [¹³C II] simultaneously. For the analysis, we combined the [¹³C II] F = 1−0 and F = 1−1 hyperfine components as they do not overlap with the [¹²C II] line in velocity. Results. Three positions in N159 and N160 show an enhancement of [¹³C II] compared to the abundance-ratio-scaled [¹²C II] profile. This is likely due to the [¹²C II] line being optically thick, supported by the fact that the [¹³C II] line profile is narrower than [¹²C II], the enhancement varies with velocity, and the peak velocity of [¹³C II] matches the [O I] 63 μm self-absorption. The [¹²C II] line profile is broader than expected from a simple optical depth broadening of the [¹³C II] line, supporting the scenario of several PDR components in one beam having varying [¹²C II] optical depths. The derived [¹²C II] optical depth at three positions (beam size of 14″, corresponding to 3.4 pc) is 1−3, which is similar to values observed in several Galactic sources shown in previous studies. If this also applies to distant galaxies, the [C II] intensity will be underestimated by a factor of approximately 2.