If you currently have a granite or solid surface countertop, it can be done. Please keep in mind that with an under mount sink, the edges of the countertop will show and depending on the sink, they may have to be cut. Either way, there will be a rough edge that will need to be polished to a finished product.
So, it can be done but it will not be an easy task and can be pretty messy, especially in a finished place such as a kitchen.
Plus keep in mind you will need to find a sink bigger than the one you have now, so there will be material to support it and cut to.
If you have a Formica top you will not be able to have an under mount sink due to the material.