Check out this fast food joint called Vishu Chats. They have an excellent variety of chats that are really reminiscent of the good old north Indian chats. Though there is a local flavour to most of the chats, it's tolerable.
Cafe Evo is also a decent option if your looking for tasty chats. They also serve South Indian cuisine along with some great non-veg dishes so there's something for everyone.
One of the best places in Chennai to get chats, fast food and other snacks is Kailash Prabhat. The Non-AC restaurant is decent enough for a quick bite.