In a large saucepan saute chicken, onions, olives and capers over medium heat. Pour in a little juice from the olives to add more olive flavor. As the onion begins to turn clear and the chicken begins to brown, add tomato sauce. Saute mixture until everything is lightly cooked. Reduce heat to low.
In a small saucepan melt shortening over medium heat; add achiote seeds. When the shortening turns red remove it from the heat and strain out the seeds. Mix oil into chicken/tomato mixture. Add the boiling water to the mixture, increase the heat to medium high and bring to a boil, stirring well.
Add the rice to the boiling mixture and continue to boil for about 3 minutes. Reduce heat to low and continue cooking for about 30 minutes, or until rice is tender and has absorbed the liquid, stirring occasionally. Remove from heat and let stand for 10 minutes.
Transfer mixture to a large bowl and serve immediately.