Kentucky Code Section 527.040 (which I've cut and pasted below) prohibits the possession of any firearm by a convicted felon, and there does not appear to be any exception in the law for hunting purposes.
If you have a felony conviction on your record that is after 1994, I believe you would be in violation of the law if you owned any firearm at all, for any reason. The only solution would be to apply for a governor's pardon. Depending on what your conviction is for, how old it is, and what you've done since then to show you are a law-abiding and reformed citizen, an attorney in your area may be able to help you file the necessary papers to get a pardon. If you were to secure a pardon from the governor, then I believe you would no longer be barred by this statute from owning a firearm.
Be aware that there are also federal laws against possession of firearms by convicted felons, although the likelihood of your being federally prosecuted for owning a hunting rifle is exceedingly small, assuming you are operating within state law and not using the rifle in some way that affects interstate commerce.
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Possession of firearm by convicted felon -- Exceptions.
A person is guilty of possession of a firearm by a convicted felon when he
possesses, manufactures, or transports a firearm when he has been convicted of a
felony, as defined by the laws of the jurisdiction in which he was convicted, in any
state or federal court
and has not:
(a) Been granted a full pardon by the Governor or by the President of the United
(b) Been granted relief
by the United States Secretary of the Treasury pursuant to
the Federal Gun
Control Act of 1968, as amended.
Possession of a firearm by a convicted felon is a Class D felony unless the firearm
possessed is a handgun in which case it is a Class C felony.
The provisions of this section shall apply to any youthful offender convicted of a
felony offense under the laws of this Commonwealth. The exceptions contained in
KRS 527.100 prohibiting possession of a handgun by a minor shall not apply to this
The provisions of this section with respect to handguns, shall apply only to persons
convicted after January 1, 1975, and with respect to other firearms, to persons
convicted after July 15, 1994.
Edited by BenPrince on 10/18/2009 at 6:46 AM EST