Omega lockout screen
The Omega Directive (denoted by Ω) is a classified Starfleet general order requiring the Captain of a starship to notify Starfleet Command immediately upon detection of an Omega molecule.
The directive authorizes the use of any and all means to destroy an Omega molecule. The Omega Directive was deemed necessary because of the extreme power and the threat to interstellar civilization posed by even a single molecule. The Omega Directive also authorizes a starship captain to violate the Prime Directive if necessary to erase knowledge of the existence of Omega. Knowledge of the Omega Molecule and the Omega Directive is restricted to Starfleet officers ranking Captain or higher, and then only on a need-to-know basis.
Background
In 2269, a team of 127 Federation scientists, led by Professor Ketteract, were working on a top secret experiment entitled "Project Omega" at a classified research center in the Lantaru sector. The project's goal was to create an inexhaustible energy source which would end all needs for all other sources of energy, hence the name Omega. The research showed a single molecule of Omega contained the same power as a warp core, which led Ketteract to believe a small chain of Omega molecules could sustain a civilization indefinitely. Ketteract, along with various cosmologists, theorized that the Omega molecule once existed in nature for an infinitesimal period of time at the exact moment of the big bang. Ketteract even postulated Omega was the primal source of energy for the explosion that began our universe.
Research station destroyed by Omega molecules
The scientists were able to synthesize a single Omega molecule, but only for a fraction of a second before it destabilized, destroying the research center and killing all 127 scientists. An unexpected secondary effect was the rupture of subspace extending out 3.2 light years. Through further theoretical tests, Starfleet Command concluded a chain reaction involving a handful of Omega molecules could devastate and/or destroy subspace throughout an entire quadrant, causing warp travel to become an impossibility; this would effectively end interstellar travel for spacefaring civilizations in the region.
Starfleet, in an attempt to keep all information of the destruction of the research center and the subspace rupture secret, suppressed all knowledge of the experiment. They subsequently fabricated the story of a natural phenomenon occurring in the Lantaru sector which made warp travel impossible in a radius of 3.2 light years.
Omega molecules being destroyed
Starfleet, in 2270, then enacted the Omega Directive. Named after the last letter in the Greek alphabet and chosen to represent a threat not only to the Federation but to the entire galaxy, the Omega Directive states that any and all Omega molecules found are to be destroyed at all costs. Starfleet concluded that since Omega is believed to be the most powerful substance known to exist, information of it could not fall into the wrong hands. Starfleet then restricted access to the Omega Directive to Federation captains and flag officers. When an Omega molecule was encountered, all other priorities would be rescinded, including the Prime Directive, and Starfleet would be informed of the discovery. Starfleet would then send in a specialized team authorized to use whatever means necessary to deal with the crisis and destroy the molecules.
The only known execution of the Omega Directive occurred in the Delta Quadrant on Stardate 51781.2 in 2374 by Captain Kathryn Janeway on board the USS Voyager. Although the Directive was adapted to meet the specialized needs of a ship far from Starfleet, the molecules were destroyed as ordered, even those naturally stabilizing just prior to their destruction. (VOY: "The Omega Directive")