https://localhost:7777 Browser warning

[Andrey P.]

Hello.
I've developed openSSL server. It must work with a local browser using https
connections.
For example, browser send URL https://localhost:7777/page.html, and server
send back HTTP-packet.
This scheme works fine except a unpleasant side effect: each time browser
shows the warning message about the server's certificate. Sure I use
self-signed certificate, but I suppose that authorized certificate for
"localhost" is impossible to get.

How can I solve this trouble?

Thanks.
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Is it possible for you to add your own certificate into the trusted chain?