You can apply for citizenship on your own. Although your divorce will not automatically deny you your ability to apply for citizenship, they may ask you follow up questions about the divorce in your interview. As you said, they want to make sure you did not get married just to get legal status, although eight years of marriage seems pretty legitimate. I suggest you contact an immigration attorney to further help you with this process.
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I agree with my colleague. Remember that at the naturalization interview USCIS can inquire into the basis for the permanent residence and basically ensure that you had legitimately obtained status because LPR status is one of the prerequisites to obtain naturalization. Your entire immigration history could be inquired about as well as good moral character. You should consult with an immigration attorney with experience handling naturalization in your area. Be sure you meet all requirements for naturalization before applying. See for example this website http://www.ailalawyer.com/
No attorney-client relationship is created or implied by this communication in any way. Consult a competent immigration attorney preferably one who is a member of the American Immigration Lawyers Association (AILA).
You can apply.
Divorce should not affect application
There should be no interview regarding your marriage - unless someone contacts CIS with damaging information.
Samuel Ouya Maina, Esq. 415.391.6612 firstname.lastname@example.org Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104