  We report silicon delta doping in Gallium Oxide (\b{eta}-Ga2O3) grown by
plasma assisted molecular beam epitaxy using a shutter pulsing technique. We
describe growth procedures that can be used to realize high Si incorporation in
an oxidizing oxygen plasma environment. Delta doping was used to realize thin
(12 nm) low-resistance layers with sheet resistance of 320 Ohm/square (mobility
of 83 cm^2/Vs, integrated sheet charge of 2.4x10^14 cm^-2). A single
delta-doped sheet of carriers was employed as a channel to realize a field
effect transistor with current ID,MAX =292 mA/mm and transconductance gM = 27
mS/mm.
