Is it true that the cronic use of the supplement coenzyme Q-10 can
cause an increase in the speed at which one's cells age? If so will
this impact one health or shorten one's life?

I have heard otherwise. To my understanding of Q-10 and what its
function is to begin with- it is an antioxidant. This means that it
will theoretically decrease the rate of "aging" on a cellular level.

Now, as for "chronic use" of Q-10: it has not yet been documented
whether the supplement is has positive or negative affects when used
in coordination with many treatments that realistically would
accompany its use. The human clinical trials that have been performed
have not measured on ANY level the possible negative cellular effects
of the enzyme itself.

To answer the other half of your question (although it has nothing to
do with my response above, really): A drug which impedes a cells
"lifetime" would not be directly negative in terms of "shortening ones
life." A short cell life may affect things such as visible aging signs
and capacity to heal and perform. So indirectly, it could decrease
life capacity, but not life span.