It shouldn't affect your AAoA for 7-10 years after closure, so you're good there.
As for the Util - it may not affect that much, either. If you have $3K in credit, it'll affect it more than if you have $100K. However, you're using 33% of it now, so if you pay it off, the net loss of open credit is really only $200. (Since that's what was available) If you have a lot of small limit cards, sock drawering it might be a good idea instead of closing if there's no annual fee. If your other cards are higher limits, you probably won't see much change from closing it.
(
My wife and I both have Kohl's cards and for the time we've decided to keep both since sometimes she'll get 30% off coupons while I get 15% or 20%, and vice versa. The coupons that are only valid with the Kohl's card make it worthwhile for us to keep. Their prices only make sense when there is a sale AND you have % or $ off coupons, and the Yes2You Rewards and Kohl's Cash also help. Mine also started at the insultingly low $300, but it seems to be somewhat standard for most people here that they have a 300 > 700 > 1500 > 2500 > 3000 incremental CLI policy. If it's a place that you actually do shop, I think it's valuable as long as you PIF each month and don't pay their 20%+ interest.
In my experience, paying in full after making a purchase or two every few months they will grant CLIs every 6 months until you hit the $3k cap. I know at least one member here claims to have a Kohl's account with a higher limit, but the rest of us get those "You already have the maximum credit line offered for this account" message from Capital One in the mail after asking for a CLI. What are the reasons they send you in the mail after a denial? Unless you have recent negatives, I can't see it not growing eventually.
Edit: Forgot to add, my CLIs for Kohl's were all when I had 30-85% total utilization so that alone should not be a major barrier.
Requested CLI from Kohls yesterday. It was a HP and my request was declined. I've had this card for over a year now, and still stuck at $300 when all my other cards have gone up and up. I have no recent negatives at all.
Plus, Kohls is overpriced. I guess it's to make up for the phony "Kohls Cash" they issue. 
Wow. Other than when I applied for the card, I never received a HP. I used to hit the CLI request button monthly.
@K-in-Boston wrote:Wow. Other than when I applied for the card, I never received a HP. I used to hit the CLI request button monthly.
How long ago did you have your card? Kohl's used to issue their own cards (or at least through an arm they owned), but now CapOne does them. (No idea how long, but I think it's been a while)
All the CapOne CLI discussions I've seen are for their Visa/MC products - this is the only retail one of theirs I know of, but it's odd they'd have such different policies.
We still have both. I don't think I opened mine until about 2013 or 2014. I think my wife has had hers since the early or mid 90s, not originally CO of course. The last time I submitted a CLI request was a few months ago. Did it every month until I got the "maximum credit line" letter. Again, never a HP.
@Anonymous wrote:My credit profile is pretty decent. No baddies, one late payment from 2014. Only other bad thing is high utilization which I'm working to get down. I have a mix of credit cards and loans. None past due or anything like that. I have JCP, Lowe's, Walmart, Kohl's, Care Credit, 2 local credit union credit cards, 2 personal loans under my name (co signer), one car loan thru my credit union, big student loan. My problem is, is that Kohl's is doing me no good. They will not raise my limit. I had a zero balance but decided to charge dad's Christmas present. Limit is $300. Current balance is $101 which I'm about to pay off. I opened it Sept 2015. I know closing it will impact my AAoA and my % of available credit, but my goodness, I see no other benefit. At least Lowe's and Walmart , I can get some type of discount. JCP may not have credit rewards, but their prices are sure cheaper than Kohl's. Any thoughts on whether or not I should just close the Kohl's account?
As heyryan stated, closing the card would not impact AAoA as closed trade lines are still counted in the formula. On closed accounts, the limit is no longer taken into account for available credit. So for people with less available credit that carry balances, closing a card would impact their debit to credit ratio. It does not sound like you would be impacted much in your situation.
How have you been requesting your CLI's? Online? Phone? My Kohl's is almost 16; I was approved with a SL of $1,500 and it stayed that way up until 2015 when the forums reported that Kohl's added the CLI button online and offered SP CLI's. I clicked it, entred my income and housing situation and they increased it to $2,500 with no HP. So, if you have not already, try going online to request the CLI.
The only thing the Kohl's charge is good for is the discounts. Sometimes its 15%, sometimes higher, up to 30%. Of course, Kohl's is shady and sometimes their "sale" prices are higher than the normal prices so who knows when you are actually winning. If you aren't using it much anymore, than I'd say adios to the Kohl's. I really should close mine since I can't stand that store. 
@MrsCHX wrote:...it seems a lot of people have the idea that closing cards affects AAoA. And I'm just curious where that comes from.
Opening cards affects AAoA but not closing. At any rate, it's good to assess OP and figure out what you need and what you don't.
Most likely that comes from the Vantage 3.0 model, which does not count closed accounts (probably one of many reasons that my FAKO scores are usually 100 points lower than my FICO 08 scores). Closing cards can affect AAoA on actual FICO scores years down the road when they fall off of the CRs. For a hefty chunk of the MyFICO population, it's not going to matter much.