Simple telnet chat server in Python

I was reading about sockets and found a nice exercise to try: a simple chat server that echoes input. This appears to be a common exercise and I have found several examples such as chatserver5.py and some SO questions. The problem is I can only connect when using telnet localhost 51234 and not telnet 192.168.1.3 51234 (where 192.168.1.3 is the network IP of my "server"). Needless to say, I can't connect from another machine on my network. I get the following output:

Trying 192.168.1.3...
telnet: connect to address 192.168.1.3: Connection refused
telnet: Unable to connect to remote host

Here is my code:

import socket, threading

HOST = '127.0.0.1'
PORT = 51234 

s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.bind((HOST, PORT))
s.listen(4)
clients = [] #list of clients connected
lock = threading.Lock()


class chatServer(threading.Thread):
    def __init__(self, (socket,address)):
        threading.Thread.__init__(self)
        self.socket = socket
        self.address= address

    def run(self):
        lock.acquire()
        clients.append(self)
        lock.release()
        print '%s:%s connected.' % self.address
        while True:
            data = self.socket.recv(1024)
            if not data:
                break
            for c in clients:
                c.socket.send(data)
        self.socket.close()
        print '%s:%s disconnected.' % self.address
        lock.acquire()
        clients.remove(self)
        lock.release()

while True: # wait for socket to connect
    # send socket to chatserver and start monitoring
    chatServer(s.accept()).start()

I have no experience with telnet or sockets. Why I can't connect remotely and how can I fix it so I can?