Is a chain fusion reaction of deuterium oxide (heavy water).possible? I think it is the case that at very high temperatures that two deuterium atoms can be made to fuse to produce helium and a release of energy. I think under appropriate physical conditions this can lead to a chain fusion reaction, although I might be wrong. My nuclear physics.lectures at university were pretty poor and long ago.
If I am not wrong about this, then my question  is: if a high enough stimulus, eg, pressure/temperature.of a critical mass of deuterium oxide heavy water were achieved, within say a hypothetical ocean of pure such heavy water, could this water be made to undergo a sustained.chained fusion reaction? I..e could this.entire hyptetical ocean detonate in a nuclear.fusion reaction
 A: 
I think it is the case that at very high temperatures that two
  deuterium atoms can be made to fuse to produce helium and a release of
  energy. I think under appropriate physical conditions this can lead to
  a chain fusion reaction, although I might be wrong

You are not: this is called ignition and is definitely possible. The conditions are difficult to achieve, you need to have enough fusion reactions that the charged particles they give off have the same amount of energy as all losses to the environment. I can't recall the energies for the D-D reaction, but off the top of my head, about 20% of the energy of D-T is an alpha, and the other 80% is a neutron. The neutron sails off without being so nice as to deposit some of its energy into the fuel, so you need to be running about 5x overall breakeven before you could potentially reach ignition, and that's assuming 100% capture of that energy.

deuterium oxide heavy water were achieved, within say a hypothetical
  ocean of pure such heavy water, could this water be made to undergo a
  sustained.chained fusion reaction

Theoretically yes, but it would be very difficult (perhaps impossible).
The problem is that "all losses to the environment" bit. One of the loss mechanisms is radiation of the fuel due to it being hot. The amount of radiative loss is a function of the atomic mass of the particle. In the case of D2O you'd have an average mass of (2*2)+16=20 as opposed to the case of pure D2 where it would be (2*2)=4. That's a whole freakload of extra losses.
You can offset this through a variety of mechanisms, the easiest just being to get a really large mass so that every bit of that "lost" radiation ultimately ends up heating the fuel mass somewhere. Then the losses are blackbody radiation of the mass as a whole. I can't recall where I saw it (I want to say Amasa Bishop's Sherwood, but I have a copy and can't find it there) but the mass for a pure D-D system is about the size of the moon. Thus D2O would be somewhere between that and a star.
