Running in a sub folder on Apache doesn't work

I can’t get Rocket.Chat to run properly in a sub folder on Apache.

With this configuration in example.conf:

<VirtualHost *:80>
        ....
        # Redirect Requests to SSL
        Redirect permanent / https://example.com
        ....
</VirtualHost>
<IfModule mod_ssl.c>
        <VirtualHost _default_:443>
        ....
        ServerName example.com
        ServerAlias example.com
        DocumentRoot /var/www/html/example/
        ....
          <Location /chat>
              Order allow,deny
              Allow from all

              RewriteEngine On
              RewriteCond %{HTTP:Upgrade} =websocket [NC]
              RewriteRule /var/www/html/example/(.*)           ws://localhost:3000/$1 [P,L]
              RewriteCond %{HTTP:Upgrade} !=websocket [NC]
              RewriteRule /var/www/html/example/(.*)           http://localhost:3000/$1 [P,L]

              ProxyPassReverse http://localhost:3000
          </Location>
        ....
        </VirtualHost>
</IfModule>

And this configuration in rocketchat.service:

MONGO_URL=mongodb://localhost:27017/rocketchat
ROOT_URL=http://example.com:3000
PORT=3000

I get a Rocket.Chat page (https://example.com/chat) but nothing works and I have this in my console

GET https://example.com/1b0d8599411c1e4f1919893c25d81fc7ac20d65b.css?meteor_css_resource=true net::ERR_ABORTED 404 (Not Found)
chat:200 GET https://example.com/theme.css?1807b422d007328786a00d34e6c63ee6022dd2b3 net::ERR_ABORTED 404 (Not Found)
chat:1138 GET https://example.com/6a61dfe05b23fcb695eea8e15f15c745e2623326.js?meteor_js_resource=true net::ERR_ABORTED 404 (Not Found)

As you can see, there’s no subfolder “chat/” in the url’s.

And when I put in rocketchat.service

ROOT_URL=https://example.com/chat/ node main.js

I get :
503 Service Unavailable

And in the Apache error log :
Fri Nov 09 16:21:16.460766 2018] [proxy_http:error] [pid 5999] [client 72.56.75.46:52090] AH01114: HTTP: failed to make connection to backend: localhost

I’m lost, I don’t understand what I’m doing wrong.

To be honest, I would always avoid operating RC in a subfolder. How about chat.yourdomain.tld instead of yourdomain.tld/chat/ ?

Unfortunately at this point I have no other choice then to have Rocket.Chat in a subfolder.