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I understand what you are saying smallfry, however some people actually pay to get a credit limit increase.
you need to weigh out your options. If you can get an increase and it may cause you a hard inquiry, yes your score may decrease but it may be made up with util% decreasing due to the increase in available credit limit.
I think you should always put yourself in the best position possible.
A couple of thousand can mean a percentage point on a mortgage for some one.
you never know.
If you are going to pay your utilization down to ~2% anyway, why bother with a CLI? I have had a chase card since 2000. I started with a CL of something like $7500 it is now at $24k. I have never asked for a cli. While they are not as regular as BoA at giving a few hundred every couple of months they do give auto CLI. At least I have gotten them. Unfortunately, as I do not follow my credit limits that carefully I cannot tell you under what circumstances I have obtained CLI.
After you pay off the card I would call Chase and say that you have been with them for 3 years (at least that is what it appears to be based on your OP). Just flat out ask if they offer auto CLI.
Good luck!