Unless you guys have some sort of different Chai drink over yonder? The only Chai I've seen here is basically as bad as hot chocolate - tonnes of sugar with some spices and nice labelling to make it seem innocent.
What you're describing might be Chai Latte, or Chai with milk and sugar.
As effingcustie said, Chai is just an Indian style of tea, often spiced. I do enjoy it more with milk though (it's the only tea that I have with milk).