In a saucepan, bring the barley and 500 ml (2 cups) broth to a boil. Season with salt. Cover, reduce the heat and simmer gently until the barley has absorbed all the broth, about 45 minutes.
Cut the asparagus into 1/2-cm (1/4-inch) lengths, keeping the tips whole. Set aside.
In a soup pot over medium-low heat, soften the carrots in the oil, about 10 minutes. Season with salt and pepper.
Add the chicken and brown over high heat, 4 to 5 minutes. Season with salt and pepper.
Add the barley, asparagus, remaining broth and oregano. Continue cooking gently, stirring frequently, until all the broth has been absorbed and the asparagus is tender. Add the spinach and stir to combine. Adjust the seasoning.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.