  A real 3-manifold is a smooth 3-manifold together with an orientation
preserving smooth involution which is called a real structure. A real contact
3-manifold is a 3-manifold with a contact distribution which is mapped to
itself by the real structure in an orientation reversing manner. We show that
every real 3-manifold can be obtained via surgery along invariant knots
starting from the standard real 3-sphere. Moreover we show that this operation
can be performed in the contact setting. Using this result we show that any
real 3-manifold admits a real contact structure. On any lens space there exists
a unique real structure that acts on each Heegaard torus as hyperellipic
involution. We show that any tight contact structure on any lens space is real
with respect to that real structure.
