No, a fission reaction is not necessary to trigger a fusion reaction, but for us on earth, it is. In the field of nuclear weapons, a fission bomb is needed to create the heat necessary to set off a fusion weapon. We have to use fission, or, rather, the energy created by that, to initiate the fusion reaction. It might be possible to use a high power source, like a laser, on a small amount of material to get fusion to occur. But we are still experimenting with this in the Tokamak, and it's far from being a done deal. Stars are, in general, massive nuclear fusion reactors. Their constant consumption of fuel powering their high rate of fusion creates a massive amount of energy, and the stars' huge gravity keeps this process from blowing the whole thing apart. No fission is needed to sustain this reaction.
