There's an Arduino tutorial on this which uses the CD4021 chip as a parallel-in, serial-out, shift register. Three pins are required on the Arduino, but you can connect up to 8 pins to the CD4021, and you just read them in one at a time. You can even cascade multiple CD4021s using the same three Arduino pins. I think the 74HC165 may also work.
https://www.arduino.cc/en/Tutorial/Foundations/ShiftIn
Edit: You might have to have high-value pullup or pulldown resistors on the shift register inputs so they won't be floating.
Also, there is the 74HC148 8-to-3 encoder, which gives a three-bit binary value for the 1 of 8 inputs which is low. You wouldn't have to clock that data in, just read the value of the three pins.