Index: Lib/io.py
===================================================================
--- Lib/io.py	(revision 58902)
+++ Lib/io.py	(working copy)
@@ -1075,7 +1075,8 @@
         self._pending = ""
         self._snapshot = None
         self._seekable = self._telling = self.buffer.seekable()
-
+        self._nl_straddle = False
+        
     @property
     def encoding(self):
         return self._encoding
@@ -1136,16 +1137,31 @@
         decoder = self._decoder = make_decoder()  # XXX: errors
         return decoder
 
+    def _adjust_chunk(self, readahead, pending):
+        if self._readtranslate:
+            if self._nl_straddle and pending and pending[0] == "\n":
+                pending = pending[1:]
+                # readahead = readahead[1:]
+                self._nl_straddle = False
+            if pending and pending[-1] == "\r":
+                self._nl_straddle = True
+            else:
+                self._nl_straddle = False
+
+        return readahead, pending
+        
     def _read_chunk(self):
         if self._decoder is None:
             raise ValueError("no decoder")
         if not self._telling:
             readahead = self.buffer.read1(self._CHUNK_SIZE)
             pending = self._decoder.decode(readahead, not readahead)
-            return readahead, pending
+            return self._adjust_chunk(readahead, pending)
+        
         decoder_buffer, decoder_state = self._decoder.getstate()
         readahead = self.buffer.read1(self._CHUNK_SIZE)
         pending = self._decoder.decode(readahead, not readahead)
+        readahead, pending = self._adjust_chunk(readahead, pending)
         self._snapshot = (decoder_state, decoder_buffer + readahead, pending)
         return readahead, pending
 
@@ -1244,6 +1260,10 @@
         res = self._pending
         if n < 0:
             res += decoder.decode(self.buffer.read(), True)
+            if self._readtranslate:
+                if self._nl_straddle and res and res[0] == "\n":
+                    res = res[1:]
+                    self._nl_straddle = False
             self._pending = ""
             self._snapshot = None
             return self._replacenl(res)
@@ -1253,8 +1273,9 @@
                 res += pending
                 if not readahead:
                     break
+            res = self._replacenl(res)
             self._pending = res[n:]
-            return self._replacenl(res[:n])
+            return res[:n]
 
     def __next__(self):
         self._telling = False
Index: Lib/test/test_io.py
===================================================================
--- Lib/test/test_io.py	(revision 58902)
+++ Lib/test/test_io.py	(working copy)
@@ -485,6 +485,10 @@
 
 class TextIOWrapperTest(unittest.TestCase):
 
+    def setUp(self):
+        self.testdata = b"AAA\r\nBBB\rCCC\r\nDDD\nEEE\r\n"
+        self.normalized = b"AAA\nBBB\nCCC\nDDD\nEEE\n".decode("ASCII")
+
     def tearDown(self):
         test_support.unlink(test_support.TESTFN)
 
@@ -741,7 +745,59 @@
                 print("Reading using readline(): %6.3f seconds" % (t3-t2))
                 print("Using readline()+tell():  %6.3f seconds" % (t4-t3))
 
+    def test_issue1395_1(self):
+        txt = io.TextIOWrapper(io.BytesIO(self.testdata), encoding="ASCII")
 
+        # read one char at a time
+        reads = ""
+        while True:
+            c = txt.read(1)
+            if not c:
+                break
+            reads += c
+        self.assertEquals(reads, self.normalized)
+
+    def test_issue1395_2(self):
+        txt = io.TextIOWrapper(io.BytesIO(self.testdata), encoding="ASCII")
+        txt._CHUNK_SIZE = 4
+
+        reads = ""
+        while True:
+            c = txt.read(4)
+            if not c:
+                break
+            reads += c
+        self.assertEquals(reads, self.normalized)
+
+    def test_issue1395_3(self):
+        txt = io.TextIOWrapper(io.BytesIO(self.testdata), encoding="ASCII")
+        txt._CHUNK_SIZE = 4
+
+        reads = txt.read(4)
+        reads += txt.read(4)
+        reads += txt.readline()
+        reads += txt.readline()
+        reads += txt.readline()
+        self.assertEquals(reads, self.normalized)
+
+    def test_issue1395_4(self):
+        txt = io.TextIOWrapper(io.BytesIO(self.testdata), encoding="ASCII")
+        txt._CHUNK_SIZE = 4
+
+        reads = txt.read(4)
+        reads += txt.read()
+        self.assertEquals(reads, self.normalized)
+
+    def test_issue1395_5(self):
+        txt = io.TextIOWrapper(io.BytesIO(self.testdata), encoding="ASCII")
+        txt._CHUNK_SIZE = 4
+
+        reads = txt.read(4)
+        pos = txt.tell()
+        txt.seek(0)
+        txt.seek(pos)
+        self.assertEquals(txt.read(4), "BBB\n")
+
 # XXX Tests for open()
 
 class MiscIOTest(unittest.TestCase):