The eSATA port on the front of your case is simply a standardized interface adapted from one of the regular SATA ports on your motherboard. The difference in port standards from SATA and eSATA has mainly to do with tighter tolerances, as well as the use of shielded cables coming from the eSATA device. All standardized motherboards of the ATX or ITS form, and their offshoots, will have either rev2 or rev3 SATA ports. Your case should have an internal cable coming from the front panel to plug into on of these SATA ports.
To answer your other question, yes, the chipset/cpu (depending on the generation) determines native SATA support, afaik. However if there is no native support, motherboard manufacturers often add 3rd party controllers to give support. However, unless you're dusting off a decade+ old motherboard, you're going to have some type of SATA support, and if you're talking about a motherboard with USB3 support, you're going to be dealing with SATA rev2, if not SATA rev3, either of which will work with the eSATA interface.