That is insanely dumb for so many reasons...
OP - it will not affect your credit score negatively. You seem to be very on top of your debt through CC's so you'll be perfectly fine. Credit card companies HATE you because they are losing money on you, but you're doing the right thing.
I just opened up that same Chase card you mentioned about a year and a half ago for the cash back reward. It was a good choice they also do a significant 1,2,3% cash back on certain purchases which is nice