I've never heard of that you get charged by closing the CD at the maturity date. No, it won't hurt your credit score.  Maybe they are referring to maintaining a linked checking account?

What I can suggest is to withdraw all money on that date.  Call them 1 day in advance.

Thanks for the response. There is one point that  I did not make it clear: I do not have a account in Chase. To do this CD, they said I have to open at least a checking account. Before I take the CD out, any amount money is ok in this checking account, but when I take out the CD after 7 months, I have to maintain $1500 in the checking account, otherwise they will charge me a $6/m service fee. So I am just asking if I can close this checking account with no harm.

fdr: Thank you for the alternative, but 12 month CD is a little bit long for me.

Based on you guys recommendations, I may consider the ING or countrywide. But I never heard those two banks. That would not be a problem , right?