Microchip has PIC variants that work between 2V and 5.5V. For example the PIC16LF87xA series. The only limit is the clock frequency is max 4MHz, or 3-5.5V @10MHz
There are a lot of PIC parts that will run at 3V. If you do not already have a part specified, go to the Microchip Advanced Part Selector (MAPS) page and select a part that meets your needs. If you do have a part that you need to use but it only runs at 5V, there may be a pin compatible part that runs at 3V.