We present a high-resolution, SparsePak two-dimensional velocity field for the center of the low surface brightness (LSB) galaxy DDO 39. These data are a significant improvement on previous H I or Hα long-slit data, yet the inner rotation curve is still uncertain due to significant noncircular and random motions. These intrinsic uncertainties, probably present in other LSB galaxies too, result in a wide range of inner slopes being consistent with the data, including those expected in cold dark matter (CDM) simulations. The halo concentration parameter provides a more useful test of cosmological models than the inner slope, as it is more tightly constrained by observations. DDO 39's halo concentration parameter is consistent with, but on the low end of, the distribution predicted by CDM.