Datasheet supply voltage range
Never ever trust the technical data given by the webpage of a distributor, they can be horrendously wrong (I've seen buck converters being sold as boost converters and voltage ratings beyond everything the chip could handle).

The datasheet on this part isn't very helpful with respect to the minimum required voltage. But the product page from TI lists the minimum required voltage:

Total Supply Voltage (Min) (+5V=5, +/-5V=10): 7V

Total Supply Voltage (Max) (+5V=5, +/-5V=10): 36V

But as others pointed out, the datasheet shows figures where the supply voltage is below 2V, so what's the right answer? As I don't know, I've asked in the E2E forum for clarification, and this is what I got as response from Ron Michallick (a TI employee (who holds no liability etc.)):


  Minimum input common mode can be as high as [VCC-] + 4V so any supply
  under 4V is very risky. The output is also not rail to rail so using
  below 7V would be quite limited.
  
  For anything less than +/-5V supply I would strongly suggest an
  alternative op-amp.