diff --git a/h11/_headers.py b/h11/_headers.py
index 878f63c..9747f31 100644
--- a/h11/_headers.py
+++ b/h11/_headers.py
@@ -64,7 +64,7 @@
 
 def normalize_and_validate(headers, _parsed=False):
     new_headers = []
-    saw_content_length = False
+    saw_content_length = None
     saw_transfer_encoding = False
     for name, value in headers:
         # For headers coming out of the parser, we can safely skip some steps,
@@ -77,10 +77,13 @@ def normalize_and_validate(headers, _parsed=False):
             validate(_field_value_re, value, "Illegal header value {!r}", value)
         name = name.lower()
         if name == b"content-length":
-            if saw_content_length:
-                raise LocalProtocolError("multiple Content-Length headers")
             validate(_content_length_re, value, "bad Content-Length")
-            saw_content_length = True
+            if saw_content_length:
+                if saw_content_length != value:
+                    raise LocalProtocolError("conflicting Content-Length headers")
+                # We have a duplicate Content-Length, so collapse it
+                new_headers.remove((name, saw_content_length))
+            saw_content_length = value
         if name == b"transfer-encoding":
             # "A server that receives a request message with a transfer coding
             # it does not understand SHOULD respond with 501 (Not
diff --git a/h11/tests/test_headers.py b/h11/tests/test_headers.py
index 67bcd7b..562baa3 100644
--- a/h11/tests/test_headers.py
+++ b/h11/tests/test_headers.py
@@ -54,6 +54,13 @@ def test_normalize_and_validate():
         normalize_and_validate([("Content-Length", "1x")])
     with pytest.raises(LocalProtocolError):
         normalize_and_validate([("Content-Length", "1"), ("Content-Length", "2")])
+    assert normalize_and_validate(
+        [("Content-Length", "1"), ("Content-Length", "1")]
+    ) == [(b"content-length", b"1")]
+    with pytest.raises(LocalProtocolError):
+        normalize_and_validate(
+            [("Content-Length", "1"), ("Content-Length", "1"), ("Content-Length", "2")]
+        )
 
     # transfer-encoding
     assert normalize_and_validate([("Transfer-Encoding", "chunked")]) == [