Step 1: Break the second down into smaller units.
One second equals 1000 milliseconds, and each millisecond equals 1000 microseconds, and each microsecond equals 1000 nanoseconds.
Step 2: Multiply these out.
$1000\times1000\times1000=10^9$, so one second contains $10^9$ nanoseconds.
Step 3: Flip it around to get one nanosecond.
If a second holds a billion nanoseconds, then one nanosecond is one billionth of a second.
\[ \boxed{\text{One billionth of a second}} \]