Heat 1 1/2 teaspoons of vegetable oil in a 12" non-stick skillet over medium heat until hot.
Add eggs and gently tilt skillet to evenly coat the bottom. It will look very thin. Cover and cook until the bottom of the omelet is barely brown and the top is just about set - about 1-2 minutes.
Slide omelet onto a cutting board and gently roll up into a tight log. Using a very sharp knife, cut the omelet tube, crosswise into 1- inch segments, leaving segments rolled up.
Heat remaining 1 1/2 Tablespoons of oil in now-empty skillet over medium heat until hot.
Add pepper mixture and cook until the mixture has been heated all the way through - 3-5 minutes.
Increase heat to medium-high, add chicken and cook till warm through, stirring constantly, till everything is thoroughly combined.
Push the chicken to the edges of the pan, to make a clear, open center well. Just recombine the molasses mixture, then pour in the center of the skillet.
When molasses starts bubbling, add the rice and cook, stirring and folding constantly; until everything is heated through and the mixture is thoroughly coated.
Off heat, garnish portions with scallions. Drizzle with lime juice. Serve immediately. Best when it is still hot.