Designing a low power PIR
You said the ideal thing would be to use a chip. Probably the easiest chip to use is the Zilog ZMOTION series microprocessors, such as the Z8FS040B. These are based off the Z80 microprocessor. They do all of the hard work for you, all you have to do is simply connect the PIR transducer to the correct pins. You'll still need the decoupling caps and the 47k resistor. They also have examples and development boards. 

https://www.zilog.com/index.php?option=com_product&amp;task=product&amp;businessLine=147&amp;id=148&amp;parent_id=148&amp;Itemid=77&amp;bk=151&amp;dvc=Z8FS040B

There is also this TI reference design that supposedly has a 10 year coin cell life: http://www.ti.com/tool/TIDA-00489?keyMatch=pir%20motion&amp;tisearch=Search-EN-Everything