diff --git a/Lib/http/client.py b/Lib/http/client.py
--- a/Lib/http/client.py
+++ b/Lib/http/client.py
@@ -746,26 +746,33 @@
         self.__response = None
         self.__state = _CS_IDLE
         self._method = None
-        self._tunnel_host = None
-        self._tunnel_port = None
-        self._tunnel_headers = {}
+        self._tunnel_host = []
+        self._tunnel_port = []
+        self._tunnel_headers = []
 
-        self._set_hostport(host, port)
+        (self.host, self.port) = self._get_hostport(host, port)
 
     def set_tunnel(self, host, port=None, headers=None):
         """ Sets up the host and the port for the HTTP CONNECT Tunnelling.
 
+        This method sends a CONNECT request to remote side. If this succeeds,
+        all further data is exchanged with *host*, with the original host acting
+        as an invisible tunnel only.
+        
         The headers argument should be a mapping of extra HTTP headers
         to send with the CONNECT request.
+
+        This method may be called repeatedly to set up a chain of tunnels.
         """
-        self._tunnel_host = host
-        self._tunnel_port = port
+        
+        self._tunnel_host.append(host)
+        self._tunnel_port.append(port)
         if headers:
-            self._tunnel_headers = headers
+            self._tunnel_headers.append(headers)
         else:
-            self._tunnel_headers.clear()
+            self._tunnel_headers.append({})
 
-    def _set_hostport(self, host, port):
+    def _get_hostport(self, host, port):
         if port is None:
             i = host.rfind(':')
             j = host.rfind(']')         # ipv6 addresses have [...]
@@ -782,18 +789,18 @@
                 port = self.default_port
             if host and host[0] == '[' and host[-1] == ']':
                 host = host[1:-1]
-        self.host = host
-        self.port = port
+
+        return (host, port)
 
     def set_debuglevel(self, level):
         self.debuglevel = level
 
-    def _tunnel(self):
-        self._set_hostport(self._tunnel_host, self._tunnel_port)
-        connect_str = "CONNECT %s:%d HTTP/1.0\r\n" % (self.host, self.port)
+    def _tunnel(self, host, port, headers):
+        (host, port) = self._get_hostport(host, port)
+        connect_str = "CONNECT %s:%d HTTP/1.0\r\n" % (host, port)
         connect_bytes = connect_str.encode("ascii")
         self.send(connect_bytes)
-        for header, value in self._tunnel_headers.items():
+        for header, value in headers.items():
             header_str = "%s: %s\r\n" % (header, value)
             header_bytes = header_str.encode("latin-1")
             self.send(header_bytes)
@@ -820,8 +827,11 @@
         """Connect to the host and port specified in __init__."""
         self.sock = socket.create_connection((self.host,self.port),
                                              self.timeout, self.source_address)
-        if self._tunnel_host:
-            self._tunnel()
+
+        for (host, port, headers) in zip(self._tunnel_host,
+                                         self._tunnel_port,
+                                         self._tunnel_headers):
+            self._tunnel(host, port, headers)
 
     def close(self):
         """Close the connection to the HTTP server."""
@@ -985,22 +995,29 @@
                         netloc_enc = netloc.encode("idna")
                     self.putheader('Host', netloc_enc)
                 else:
+                    if self._tunnel_host:
+                        host = self._tunnel_host[-1]
+                        port = self._tunnel_port[-1]
+                    else:
+                        host = self.host
+                        port = self.port
+                        
                     try:
-                        host_enc = self.host.encode("ascii")
+                        host_enc = host.encode("ascii")
                     except UnicodeEncodeError:
-                        host_enc = self.host.encode("idna")
+                        host_enc = host.encode("idna")
 
                     # As per RFC 273, IPv6 address should be wrapped with []
                     # when used as Host header
 
-                    if self.host.find(':') >= 0:
+                    if host.find(':') >= 0:
                         host_enc = b'[' + host_enc + b']'
 
-                    if self.port == self.default_port:
+                    if port == self.default_port:
                         self.putheader('Host', host_enc)
                     else:
                         host_enc = host_enc.decode("ascii")
-                        self.putheader('Host', "%s:%s" % (host_enc, self.port))
+                        self.putheader('Host', "%s:%s" % (host_enc, port))
 
             # note: we are assuming that clients will not attempt to set these
             #       headers since *this* library must deal with the
diff --git a/Misc/NEWS b/Misc/NEWS
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -195,6 +195,9 @@
 - Issue #19286: Directories in ``package_data`` are no longer added to
   the filelist, preventing failure outlined in the ticket.
 
+- Issue #7776: Fix ``Host:'' header and reconnection when using
+  http.client.HTTPConnection.set_tunnel(). Patch by Nikolaus Rath.
+  
 IDLE
 ----