Step 1: Define a perfectly black body.
A perfectly black body is an ideal surface that absorbs every bit of radiation that strikes it, reflecting and transmitting nothing. Its absorption coefficient is therefore $a = 1$.
Step 2: Recall the emission coefficient.
The coefficient of emission (emissivity) $e$ measures how good a surface is at radiating energy compared with a perfect emitter.
Step 3: Bring in Kirchhoff's law.
Kirchhoff's law of thermal radiation states that, at a given temperature, a body's emissivity equals its absorptivity: $$e = a.$$
Step 4: Apply it to the black body.
Since the black body has $a = 1$, the same law immediately gives $e = 1$.
Step 5: Interpret physically.
A perfect absorber is also a perfect emitter; nothing in nature can emit more efficiently than a black body, so its emissivity hits the maximum value of one.
Step 6: State the answer.
A value of $1$ is called unity.
\[ \boxed{e = 1\ (\text{unity})} \]