Ooohhh, that's always startling to see!
Since mom is so tolerant of you, I'd be sure to get rid of every maggot that may have been left behind on mom, the chick, and in the nest (I know, disgusting, but they don't bite through gloves or intact skin). Check through mom's feathers (if she will tolerate it), especially in the areas that she can't preen easily (around the vent, behind the tail, and the head and neck) and on the underside (breast and legs, where they would first contact her), but in her broody trance she might not pull the maggots off herself even if she could easily do so, so check everywhere if possible. Then check the chick thoroughly, especially around the vent and the navel. Then go through the nest with a fine tooth comb, or better yet just change out the nesting and bedding material all together. Most maggots are tiny on the first day, and are much larger and easier to see on the second day, so be sure to recheck once or twice daily, if mom will tolerate it. Also, be sure to remove anything that might attract flies ASAP (hatched egg shells, moist food, fresh droppings, etc). Controlling flies in the broody area would also be really important, but you can't use poisons that could harm the birds. Sticky pest strips, bug zappers, something to attract the flies to a different area where they can be poisoned away from the chickens, a bottomless wire cage covered in screen material that can be set over the nest, all those things together will likely make quite a dent in your fly population and help protect the chicks (there's probably lots of other things available also, but that's what comes to mind right now).
WARNING, this next paragraph is graphic, and quite disgusting, but relevant to this issue.
I don't mean to be an alarmist, but I've seen hundreds of (mammalian and avian) infants killed either directly or indirectly by maggots. The flies are attracted to the placenta (one of many reasons that placenta-eating is selected for in nature) or the inner egg membrane (lots of birds intentionally throw hatched egg shells out of the nest), but also get on the umbilical cord or the navel. The fly eggs hatch and the maggots eat away at the umbilical cord/navel, causing anything from blood loss, infection, pain, and sometimes penetrate into the abdomen, causing herniation or evisceration. If the babies aren't killed directly, the debilitation sometimes creates enough weakness that the infants don't nurse or eat adequately, so often die of dehydration or starvation. The maggots don't eat through intact skin, but any entry point is fair game. Once they're in the nest they can do a lot of damage, and I suspect that their smell attracts more flies to the area to lay even more eggs. Summer hatches can be challenging when flies get involved! Hopefully those were your only maggots, but I'd be very vigilant. Good luck.
Now, I'm waiting on the 6 marans eggs and I didn't notice any pips on them. Thankfully, this broody has not once pecked me and all I have to do is touch her wing and she just lets me partially lift her to look under. She's a first-timer and so sweet. Praying for the best.
