Yes, you can transfer to your United account, assuming that is what you want to do with the Chase points. You don't need to keep the United card open either, there is no reason to pay the annual fee. The miles will remain in your United account as long as you have some type of activity every 18 months. This can be earning miles, transferring some into the account, booking a flight, etc.
If you are close to the expiration date, you can buy something in the United shopping portal:
https://shopping.mileageplus.comI'd probably grab the Chase cards first, but then you can look at the Delta cards available through American Express, just wait until they are offering a high bonus. The American Express cards that offer MR points can be transferred to Delta (Platinum, Premier Rewards Gold, and business versions).