Is this resistor needed in this opamp circuit?
It's there to match the impedance on both inputs, which minimises offset voltage in addition to the inherent input offset (to be thorough, the resistor in question is not actually necessary if the divider resistor values are chosen correctly, as Olin notes in his answer)

Since the same current flows through each input*, if the impedances are matched then the same voltage drop will be caused on each input and cancel out.
*This only holds true for opamps with matched input currents, which is not always the case. An excellent reference which discusses this and much more is Opamp Applications by Walt G. Jung.

To give an example, if we take a simple opamp non-inverting buffer, the opamp having an input impedance of 1 Megaohm (to exaggerate the effect, though you do get opamps with similar input resistances)
Vin is at 1V:  



R1 is the input impedance at 500k. Often you see buffers with no Rf, just the output wired straight to the inverting input. However to match the offset voltage correctly we need an Rf equal to the input impedance.
To show the offset effect, we sweep Rf from 1 ohm to 500 kOhm:



Note how with an Rf of 1 ohm, Vout is ~500mV offset from Vin. As Rf increases toward 500k, we can see the offset heads to zero.     

If you look on page 13 (4.7) you will see an explanation of this with the same circuit used as an example.
As Olin notes, at typical 1pA input current, unless you have huge impedances there's no point doing this as the effect will be tiny compared to the inherent offset. It doesn't hurt to get into the habit of thinking about it though.     

However, a high temperatures the input bias current can increase quite dramatically, in which case the effect can become more noticeable again. For the MCP6421 the current increases to 1100pA at 125degC. So make sure you take all this into account when deciding what is necessary.