I don't have any orzo on hand. What do you think would be a better substitute: another small pasta, or white rice?

I think that you could get away with using long-grained rice; or if you have pastina, that might work as well.

I don't think rice would be a good substitute for the recipe as written, because the liquid ratio would be off. However, there is nothing saying you couldn't do the dish without the rice, cook the rice- or even another pasta shape - separately, and then marry the two when the chicken is done. That way you can capture the yummy juices, and not have to worry about adjusting liquid ratios.