When in doubt, native speakers usually use “less”, even in situations where the grammarians would insist otherwise. (The rule about using “fewer” in the plural is relatively recent.) When speaking of a length of time, we usually use singular notional agreement, since “time” is uncountable in this sense, and it’s just one *length* of time (that happens to be measured in year).
One week is a long time. Seven days is a long time.
Now, if we want to emphasize that we are referring to the individual years, then we can use the plural: “During the last century, they won the championship in fewer than 20 years.” Note that the meaning is different from “in less than 20 years” (which does not refer to the individual years, only to the length of time).
Edit: Fixed typo.
PS: We can sometimes use "under" instead of "less": "He became a doctor in under four years."