So I have a Chase Bank Visa. Issued in the USA. No unionpay logo on the card.

In Kunming, I have successfully used this only at the nanpingjie Carrefour to pay for goods. I tried yesterday at Metro, and the girl at the counter said Metro could only take unionpay visas.

Where else in Kunming has anyone had success paying with a non unionpay Visa issued outside of China? Shops? Restaurants?

I paid with visa at a jewellery shop in the centre of town no problems. No one batted an eyelid. That was a NZ issued visa, I assume that all western visas would be OK.

Unionpay and VISA are not the same thing. It wouldn't make sense that only a VISA card issued in one country could be accepted and not one from another country at a given business establishment.

Airlines, better hotels, some upper class restaurants, all Carrefour and Walmart stores, etc. all accept VISA cards. Unfortunately, not as many retailers as there should be accept credit cards in general in Kunming, but at least you can use them in a number of places.

I cannot use my UK Visa in Metro.
I can however use my China Merchants Bank Visa credit card (not debit card) in Metro.

Seems Metro only accepts China issued Visa.

I was not able to use my foreign visa at the Walmart in Xiaoximen or another Carrefour that was not the nanpingjie one. The difference the clerk said was that the nanpingjie Carrefour is the flagship store for Kunming.

I have had the problem in other cities and other retail outlets too.

Rule of thumb for bankcard use in China: if it's partially aimed at foreign tourists, it will probably accept foreign bank- or visa-cards.

Examples:
Carrefour: local visa card yes, foreign visa card no
Jewellery shop: foreign cards yes
Agricultural Bank of China in 南沙: local cards yes, foreign card no
Agricultural Bank of China in 新街 (a much smaller town 40km further up in the mountains but renowned for its rice terraces): foreign visa accepted

It has to do with retailers not wanting to pay for the % fee.
Credit Card companies make their money on a % of sale from the retailer AND crazy interest from the consumer..

I assume the Western credit card companies charge a higher % than Chinese bank Credit cards..

Another factor is if the retailer or ATM is connected to the international system.

I have shopped at numerous Carrefours and they all accepted my VISA card issued abroad. For example, the store on Longquan road always accepts my VISA or when I use it, Mastercard. One of my Mastercard credit cards uses an in built chip system and I sometimes have to explain to the clerk that it needs to be inserted into the machine and not swiped in this case.

Thanks. The carrefour on Longquan did take my card. I assume you're correct that they all should. The carrefour that couldn't take mine was very new; meaning the clerk was probably very new too and unexperienced.