Rinse the rice in a fine-mesh strainer and add to a rice cooker. Add 2 1/2 cups of the chicken broth. Cover the rice cooker and turn it on.
Meanwhile, cut the chicken breast in half lengthwise, then cut each half into 1/4-inch-thick slices. Transfer the chicken to a shallow bowl. In a small bowl, mix the olive oil with the tarragon, salt, pepper and the lemon juice and zest. Drizzle the marinade over the chicken slices, stir to coat and set aside.
When the rice is done (and the machine switches off), remove the lid and spread the chicken in a single layer over the rice, then sprinkle the onion and garlic over the chicken. Spread the asparagus in an even layer on top, then pour the remaining 1/2 cup of chicken broth around the edge of the rice cooker; cover the rice cooker. Turn on the rice cooker again and cook until the chicken is done, about 10-15 minutes. Toss the mixture well before serving.