The most common and most likely answer to this crossword clue is the 10 letter word STOCHASTIC
I've seen this crossword clue in The Guardian
S
T
O
C
H
A
S
T
I
C
Buddy explains!
The straight part
We know that "Being governed by chance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case being governed by chance = stochastic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does STOCHASTIC mean?
STOCHASTIC adjective- Random, randomly determined.