Random fields coupled to an order parameter describing one or more broken continuous symmetries have been investigated since the early 1970's - from the destruction of long-range order of the Abrikosov vortex lattice in type II superconductor to ferromagnetism in a materials random magnetic disorder. In this talk I argue that the quantum liquid phases of 3He infused into silica aerogel provide a unique system for studying the struggle between orbital order of Cooper pairs, and disorder characterized by random anisotropy. This competition leads to remarkable new chiral superfluid phases exhibiting broken time-inversion symmetry, space parity, and as I argue, a novel phase that has finite range orientational order in two dimensions, but long range order in a third dimension. This phase is the realization of a biaxial-chiral phase with finite-range orientational correlations due to the random anisotropy field of the aerogel medium. These conclusions are supported by theoretical analysis of the phase diagram and NMR spectra of superfluid 3He infused into anisotropic aerogel.