You need an opamp that is true rail to rail on both input and output. The old LM324 can do ground on the inputs( actually it will go to -0.6V happily, but caveat emptor there), and will get close to ground if you use a pull down resistor on the output to actively pull it down( it then has an output stage that runs happily in class A as a current source). Will not go to 0V exactly, but will do well depending on the load. otherwise you do need a negative supply, anything more than about 2V will do, as the internal transistors need some voltage across them.