Yes the milk is boiled, otherwise it wouldn't make chai.
Be more concerned about the cleanliness of cups and glasses etc, or get a throw-away paper cup. Just drink it from a reasonably clean-looking place. If you've eaten the food there, don't worry about the tea!
I think it is reasonable to ask questions about food safety when visiting India, I know I have :D
Some folk are nervous travellers, but better to travel with anxieties than not at all, methinks?
Because the milk is boiled up with the water, it should be safe to drink. I assume that is the reason behind chai making in the first place?
Talking about clean cups, etc, reminded me of our first visit to India back in 1983. Aboard a train, a chai guy is coming through, he is rinsing each glass after use in a rather dodgy looking bucket of water, before refilling. We decided to hand him our pristine steel drinking cups to be filled instead. Guy "kindly" rinses them in his bucket before filling with chai. We survived... :D
I recall reading once that incidents throat cancer among drinkers black tea with milk in India was less than drinkers of plain black tea in China. This was due to the proteins in the milk binding with the tannin from the tea, instead of the tannin binding to the tissues in the throat. Tannin in more concentrated form is used in the curing of leather.
I agree -- chai is safe, but utensils may not be. Carry your own lidded to-go cup. (Also better for the environment.) Every eatery has a handwashing sink of some sort where you can clean it. Someplace there is a great essay about rating food establishments in India by observing how many rags are in use for the griddle, the tables, the hands, the floor, the baby, the dogs. Below the 3-rag level it's best to eat elsewhere. In the US one judges roadside diners by how many trucks are in the parking lot and how many calendars are on the wall (the more, the better).
Kathy "Real Happiness Lies in Making Others Happy" - Avatar Meher Baba
Well, quite possible not. I always make that way, but when you go to a tea stall in this part of the world you will find that the milk is simmering away in its own pot. The tea master will mix them when serving, pouring the tea through a strainer that looks like a sock that has twenty years of tea leaf embedded in it. Perhaps it is!