Rinse the rice well with cold water. Place it in a medium bowl with enough lukewarm water to cover it by an inch, stir in 1 teaspoon of the salt, and set aside to soak.
Remove the excess fat from the chicken. Finely chop about 3 tablespoons fat and set aside. Traditionally the skin is left on, for extra flavor and succulence; remove and discard it if you wish. Use a cleaver to chop the chicken into approximately 2-inch pieces, leaving the bones in. Rinse and set aside.
Peel the daikon and grate it on a coarse grater, or cut it into match-sticks (thinly slice it on a long diagonal, then stack the slices and cut into matchsticks). You will have about 2 cups. Set aside.
Heat the oil in a large wide heavy pot over medium heat. Add the reserved chicken fat and render it (over medium heat, the fat will gradually melt into the oil, leaving some small crispy cracklings). Once the fat has melted, scoop out the cracklings and save for another purpose (such as a topping for congee or for flatbreads). Raise the heat to high, and when the oil and fat are nearly smoking, add 1 teaspoon of the salt. Carefully slide the chicken pieces into the oil and start to brown them, turning occasionally. (If your pot is not wide enough, you may have to brown the chicken in 2 batches; then return all the chicken to the pot.) After several minutes, add the onions. Cook until the chicken is browned on all sides, then add the daikon and tomatoes and stir well. Lower the heat slightly and cook for about 5 minutes, stirring if the vegetables are sticking at all. The daikon should have softened and the tomato will be starting to disintegrate.
Add the water and the remaining 1 teaspoon salt, raise the heat, and bring to a vigorous boil. Lower the heat to medium and boil gently, partly covered, for 10 minutes. Taste the broth and adjust the seasoning if necessary.
Drain the soaked rice and sprinkle it into the broth. The liquid should cover the rice by ½ inch; add a little hot water if necessary. Bring to a boil, then cover tightly, lower the heat to medium, and cook for 5 minutes. The water will now be just level with the top of the rice. Distribute the pumpkin pieces over the rice. Cover tightly once more, lower the heat to very low, and cook for 30 minutes.
Remove the pot from the heat and let stand for 10 minutes before removing the lid.
Traditionally pulao is served on a platter, the rice mounded and then the pumpkin and chicken pieces placed on top, but we like to serve it straight from the pot. If you serve it on a platter, use tongs to lift out the chicken pieces and the pumpkin (the cooked cubes of pumpkin are very tender, so be careful not to mash them), and set them aside. Use a wooden spoon or spatula to mound the rice on the platter, then place the pumpkin and chicken pieces on top. Traditionally guests, after washing their hands, eat with their hands, helping themselves directly from the platter. If your guests are not comfortable eating this way, serve them individually, or put out several serving spoons so they can serve themselves from the platter, and provide spoons and forks to eat with.
Put out several condiment bowls of the vinegar, together with small serving spoons. Invite guests to drizzle a little vinegar onto their rice. If you like, put out wedges of lemon to be squeezed over the chicken and rice to taste, and put out a pepper mill.
Quinces are a common fruit in the Silk Road oases in the autumn. They look like knobby yellow apples and are very hard. They have a delicious sweet-acid flavor when cooked and, when available, are often used in Uighur pulaos as a foil for the meat. You can include 1 or 2 small quinces, peeled, cored, and cut into 1-inch chunks, instead of the pumpkin or in addition.