  We report results of experiments with liquid $^3$He confined in a high
porosity anisotropic nanostructure which we call planar aerogel. This aerogel
consists of nanofibers (with diameters $\sim10$ nm) which are randomly oriented
in the plane normal to the specific axis. We used two samples of planar aerogel
prepared using different techniques. We have found that on cooling from the
normal phase of $^3$He the superfluid transition in both samples occurs into an
equal spin pairing superfluid phase. NMR properties of this phase qualitatively
agree with the properties of the superfluid A phase in the anisotropic
Larkin-Imry-Ma state. We have observed differences between results obtained in
the presence and absence of solid paramagnetic $^3$He on the aerogel strands.
We propose that these differences may be due, at least in part, to a magnetic
scattering channel which appears in the presence of solid paramagnetic $^3$He.
