Balance chasing is when the credit card company cuts your credit limit to just above your balance. This appears to happen most frequently after you make a large payment to reduce your balance. This can hurt your credit score by making you have a larger portion of your available balance occupied. How can you avoid this potential credit score ding? Don't keep any balances of course.
http://www.creditmattersblog.com/2008/10/chasing-balance-what-it-is-and-why-it.html