We precisely constrain the inner mass profile of A2261 (z=0.225) for the first time and determine that this cluster is not "overconcentrated" as found previously, implying a formation time in agreement with {Lambda}CDM expectations. These results are based on multiple strong-lensing analyses of new 16-band Hubble Space Telescope imaging obtained as part of the Cluster Lensing and Supernova survey with Hubble (CLASH; Postman et al. 2012, Cat. J/ApJS/199/25). Combining this with revised weak-lensing analyses of Subaru wide-field imaging with five-band Subaru + KPNO photometry, we place tight new constraints on the halo virial mass M_vir_=(2.2+/-0.2)x10^15^M_{sun}_h^-1^_70_ (within r_vir_{approx}3Mpc.h^-1^_70_) and concentration c_vir_=6.2+/-0.3 when assuming a spherical halo. This agrees broadly with average c(M, z) predictions from recent {Lambda}CDM simulations, which span 5<~<c><~8. Our most significant systematic uncertainty is halo elongation along the line of sight (LOS). To estimate this, we also derive a mass profile based on archival Chandra X-ray observations and find it to be ~35% lower than our lensing-derived profile at r_2500_~600kpc. Agreement can be achieved by a halo elongated with a ~2:1 axis ratio along our LOS. For this elongated halo model, we find M_vir_=(1.7+/-0.2)x10^15^M_{sun}_h^-1^_70_ and c_vir_=4.6+/-0.2, placing rough lower limits on these values. The need for halo elongation can be partially obviated by non-thermal pressure support and, perhaps entirely, by systematic errors in the X-ray mass measurements. We estimate the effect of background structures based on MMT/Hectospec spectroscopic redshifts and find that these tend to lower M_vir_ further by ~7% and increase c_vir_by ~5%.