The alkynyl carbon chemical shift (CS) tensors for 2-butyne-1,4-diol are reported, based on analyses of the carbon-13 NMR spectra of stationary-powder and slow magic-angle spinning (MAS) samples for which the alkynyl carbon nuclei are enriched in 13C. NMR spectra of slow MAS samples exhibit spinning-frequency-dependent fine structure typical of crystallographically equivalent but magnetically distinct nuclei. Simulated spectra of slow MAS samples of this two-spin system are particularly sensitive to the relative orientations of the CS tensors. In addition, the value of 1J(13C, 13C), +175 +/- 10 Hz, is determined by examination of the total NMR lineshape of slow MAS samples. The CS tensors are almost axially symmetric, delta11 = 158.9 +/- 1.0 ppm and delta22 = 155.7 +/- 1.0 ppm; the direction of greatest shielding is approximately along the alkynyl C-C bond, delta33 = -57.8 +/- 2.0 ppm. Both the magnitudes of the principal components of the CS tensors and their orientations are in agreement with those predicted from first-principles calculations at the HF and MP2 levels of theory. This study demonstrates the importance of examining the NMR spectra of homonuclear two-spin systems with and without MAS under a variety of conditions (e.g., two or more applied magnetic fields and slow MAS).