No. If you are a convicted felon, it is only legal for you to possess a firearm in your home (and it would be illegal under federal law for you to even possess a firearm at all). Since a concealed handgun permit allows you to carry that weapon in public, you would not be eligible.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.