I sympathize with you.
Our cats have been equally long-lived, and when you spend that many years living closely with someone who asks so little and gives so much in return it's almost as bad as losing a spouse. I've had 8 cats in my life, usually several at a time so that they would always have companions when we were away at work. When one passes, the others keep searching the house for the missing one, scratching at closed doors and watching at the windows. Every cat has a unique personality; I miss them all.
It's hard to have to put down any animal, but it's better than letting one live in pain as I did once years ago. I couldn't bear to part with her, and spent a lot taking her to the vet to try to keep her. The last time she stayed with the vet for a week without getting better, so we decided to bring her home. She recognized where she was, sniffed our other cat, gave my wife a greeting meow, started purring, and fell over dead. Never again will I let that happen to someone I love, and I hope that no one tries to keep me alive past my time.
Fortunately (or unfortunately) for us, there are so many equally-lovable love-seeking homeless cats. Honor Chloe's memory by adopting one, and care for it the way she cared for you.