Problem reading from MAX11060 16bit ADC

I guess you're doing this with an Arduino UNO (as didn't specified another model). You should set the SS pin (pin 10 on the UNO) as an output, otherwise the SPI hardware won't work correctly.

How did you wire the chip to the Arduino? The UNO runs on 5V but none of the MAX11060 pins allows more than 4V. Do you use a level converter?