You don't need the new DOs to do the chain and you pick up the first one in Beta Ursa sector, Negociate for rare Commodoties. you need some of the Gamma Quadrant commodoties to complete it.
Just started them myself, don't know about the other 3...yet.
Originally Posted by prom3theus
You can also buy them in exchange or do fleet actions (heard that, not confirmed). Depending on console type, they are in between few hundred thousands and tens of millions (10-20 depending on luck) for neutronium, phaser and disrupter.