Previous private estimators on distributions over \mathbb{R} d suffer from a curse of dimensionality, as they require \Omega(d {1/2}) samples to achieve non-trivial error, even in cases where O(1) samples suffice without privacy. This rate is unavoidable when the distribution is isotropic, namely, when the covariance is a multiple of the identity matrix. Yet, real-world data is often highly anisotropic, with signals concentrated on a small number of principal components. We develop estimators that are appropriate for such signals---our estimators are (\varepsilon,\delta) -differentially private and have sample complexity that is dimension-independent for anisotropic subgaussian distributions. We show that this is the optimal sample complexity for this task up to logarithmic factors.