I was wondering if it was possible to host a private network in geth not on the localhost. Would it be possible to connect to my private chain using a non-local ip address?
Yes, it is possible, to run your own, local network. There are different tutorials on the net, like this: https://github.com/ethereum/go-ethereum/wiki/Setting-up-private-network-or-local-cluster
Would it be possible to connect to my private chain using a non-local ip address?
That depends: if your node is bound to localhost (127.0.0.1), so it's not possible to connect from outside your computer. If the node is bound to your (one or all) "real" network interfaces, so everybody, can connect to this blockchain, depending on how your system is connected to the network. That depends on your firewall, network and/or proxy configuration of your network environment.