  We study the phase-space structure of a dark-matter halo formed in a high
resolution simulation of a Lambda CDM cosmology. Our goal is to quantify how
much substructure is left over from the inhomogeneous growth of the halo, and
how it may affect the signal in experiments aimed at detecting the dark matter
particles directly. If we focus on the equivalent of ``Solar vicinity'', we
find that the dark-matter is smoothly distributed in space. The probability of
detecting particles bound within dense lumps of individual mass less than 10^7
M_\sun h^{-1} is small, less than 10^{-2}. The velocity ellipsoid in the Solar
neighbourhood deviates only slightly from a multivariate Gaussian, and can be
thought of as a superposition of thousands of kinematically cold streams. The
motions of the most energetic particles are, however, strongly clumped and
highly anisotropic. We conclude that experiments may safely assume a smooth
multivariate Gaussian distribution to represent the kinematics of dark-matter
particles in the Solar neighbourhood. Experiments sensitive to the direction of
motion of the incident particles could exploit the expected anisotropy to learn
about the recent merging history of our Galaxy.
