Do I have to claim my child support?

Are you paying it or receiving it? If you are receiving it, then yes, you do.

I regret that I must disagree with twinkiedooter.

Alimony is deductible from income to the spouse who is paying it and taxable to the recipient.
On the other hand, child support payments are made from already taxed income. Since the tax on those payments have already been paid the recipient owes no tax on those payments.

See:
Alimony, Child Support, Court Awards, Damages (http://www.irs.gov/faqs/faq/0,,id=199747,00.html)

Agreed; child support is neither taxable to the recipient nor tax deductible to the payer.