USB Full Speed driver with MCU in DIP package
If you mean use a PIC based uC for USB, then there are a few you could use - the PIC18F4550 (and other members of the family) has a full speed USB peripheral and comes in a DIP package.
There are also many other Microchip DIP based PIC uCs with USB peripherals (PIC24, PIC32 MX2 family) and probably some from Atmel also.

If you mean implement USB in a uC without the peripheral (i.e. in software) then I don't know of anything full speed, but I believe there is a low speed library available for AVRs (V-USB).