Rice takes 30 minutes... 5 to boil the water, 20 for the rice to cook, and 5 to rest. It can sit longer too, and as long as you have the lid on the pot it'll stay warm.
Confession: I microwave most veggies, because we eat a lot of frozen (organic) veggies. If not, I steam them. That takes 10 minutes, fresh or frozen.
If you're grilling chicken (pan or real grill, boneless breasts) start everything except the veggies cooking at the same time. Keep a timer on for the rice, set it for 20 minutes once it boils. When it boils, start grilling the chicken. When you've got 8-10 minutes left on the 20 minute timer, start the veggies steaming. Everything should be done just about at the same time.
The same timing goes for pretty much any boneless chicken breasts, no matter how you cook it. When I'm baking, just to be sure I tend to overcook it, leaving it in for about 30-35 minutes. I've had too many pink ones come out of the oven. Vomitous.
Chicken is extra excellent with corn.