in a large pot, heat the EVOO over medium-high. Add the onion and cook, stirring occasionally, until golden, 5 minutes. Add the carrot and cook for 1 minute. Add the broth and tomatoes; season with salt and pepper and bring to a simmer.
in a large bowl, gently mix the chicken with 1 tsp. salt and 1/4 tsp. pepper. Roll 1 tbsp. of the chicken between your palms, forming a ball, and drop into the broth. Repeat with the remaining chicken (you should have about 20 meatballs).
Stir in the orzo and simmer 5 minutes. Add the broccoli and simmer until the meatballs are cooked through, the orzo is al dente and the vegetables are tender, about 5 minutes. Season before serving.