Index: Lib/gzip.py
===================================================================
--- Lib/gzip.py	(revision 76779)
+++ Lib/gzip.py	(working copy)
@@ -111,6 +111,7 @@
             self._new_member = True
             self.extrabuf = b""
             self.extrasize = 0
+            self.extrastart = 0
             self.name = filename
             # Starts small, scales exponentially
             self.min_readsize = 100
@@ -253,15 +254,14 @@
                 if size > self.extrasize:
                     size = self.extrasize
 
-        chunk = self.extrabuf[:size]
-        self.extrabuf = self.extrabuf[size:]
+        offset = self.offset - self.extrastart
+        chunk = self.extrabuf[offset: offset + size]
         self.extrasize = self.extrasize - size
 
         self.offset += size
         return chunk
 
     def _unread(self, buf):
-        self.extrabuf = buf + self.extrabuf
         self.extrasize = len(buf) + self.extrasize
         self.offset -= len(buf)
 
@@ -317,8 +317,10 @@
 
     def _add_read_data(self, data):
         self.crc = zlib.crc32(data, self.crc) & 0xffffffff
-        self.extrabuf = self.extrabuf + data
+        offset = self.offset - self.extrastart
+        self.extrabuf = self.extrabuf[offset:] + data
         self.extrasize = self.extrasize + len(data)
+        self.extrastart = self.offset
         self.size = self.size + len(data)
 
     def _read_eof(self):
@@ -389,6 +391,7 @@
         self._new_member = True
         self.extrabuf = b""
         self.extrasize = 0
+        self.extrastart = 0
         self.offset = 0
 
     def seek(self, offset, whence=0):
@@ -416,6 +419,14 @@
 
     def readline(self, size=-1):
         if size < 0:
+            # Shortcut common case - newline found in buffer.
+            offset = self.offset - self.extrastart
+            i = self.extrabuf.find(b'\n', offset) + 1
+            if i > 0:
+                self.extrasize -= i - offset
+                self.offset += i - offset
+                return self.extrabuf[offset: i]
+
             size = sys.maxsize
             readsize = self.min_readsize
         else: