The Brekkians were a humanoid race from the planet Brekka in the Delos system. They shared the Delos system with the Onarans, who inhabited Onara - the other inhabited planet in the system. Due to the intense solar activity of the star Delos, both the Brekians and the Onarans evolved the ability to generate electricity within their bodies.

Shortly after the founding of the United Federation of Planets in the mid 22nd century, a Federation scout ship visited the system and found both the Brekkians and Onarans on the verge of achieving spaceflight. Sometime after the ship's visit a devastating plague hit both Brekka and Onara. The Brekkians were able to cure themselves of the plague using a drug called felicium, which was produced from a plant that only grew on Brekka. They quickly realized that felicium was highly addictive and weaned themselves off the drug.

The Brekka provided felicium to the Onarans as well to help them cure the plague, but did not tell them that felicium totally cured the disease nor that felicium was highly addictive. The Brekkans manipulated the Onarans into believing that the plague could never be cured but that it could be kept at bay by regular use of felicium. They further led the Onarans to believe that the withdrawal symptons were symptons of the plague.

Over the next 200 years the Brekkians reoriented their entire economy to focus solely on manufacture and distribution of felicium. Brekkian scientists worked to refine felicium to make it more potent and more addictive while the Onarans sent freighters back and forth to transport felicium home.

In 2364 the Federation Starfleet starship Enterprise visited the Delos system to study the hyperactive star. While there they rescued the crew of an Onaran freighter along with its cargo of felicium. While both the Brekkians and the Onarans claimed the felicium was used to treat a plague, Doctor Beverly Crusher quickly saw through the Brekkian deception and realized the Brekkians were exploiting their neighbors and kept them addicted to the drugs. She and Captain Jean-Luc Picard confronted the Brekkians Sobi and Langor, who basically admitted they had been exploiting the Onarans.

Because of the Prime Directive, the Enterprise crew was unable to tell the Onarans the truth about felicium and handed the drugs over to them. However Picard refused to provide the parts or crew to repair the Onaran freighters, meaning that the Onarans would no longer be able to transport felicium from Brekka to their homeworld. The Brekkians had no freighters of their own, meaning that the drug could no longer be transported between the planets. Picard hoped that even though withdrawal would be bad, this chain of events would break the Onaran addiction and end the Brekkian exploitation of their neighbors.

After the cycle was broken, some Brekkians turned to selling felicium to other species, including the Ferengi. In 2370 Odo accused Quark of possessing some Brekkian narcotics.