Should I use an Arduino or not? I am building an electronic gadget eventually to sell.

I think the Atmega IC is used in the arduino and could this be programmed as easily as the arduino?

I'm wondering if I can use the chip and buy just what I need for my circuit, which would be cheaper as there would be no licensing obligations to the Arduino company

Cheers 
Eamonn
Short answer: Yes. After all, Arduinos are made by starting with an ATMega (or other AVR) IC. 

Longer answer: People - including myself - routinely build with a bare ATMega328p (or other MCU), programming them off-board on another system, or providing connections to allow programming them in place. Beyond that you only need the soldering skills for the chip you choose (if you're building the boards yourself). I use DIP ICs and off the shelf through-hole PCBs and hand-build one or a couple at a time. Quad Flat-Package or Surface-Mount chips are another step up in complexity for the hand-builder.