diff --git a/HISTORY.rst b/HISTORY.rst
index ba8d9b1..5f477a3 100644
--- a/HISTORY.rst
+++ b/HISTORY.rst
@@ -6,6 +6,10 @@ Release History
 
 **API Changes (Backward Compatible)**
 
+- Added a new ``ZeroLengthHeaderNameError`` that indicates that an
+  invalid header has been received. This places the HPACK decoder into
+  a broken state: it must not be used after this exception is thrown.
+
 **Bugfixes**
 
 - Performance improvement of static header search. Use dict search instead
diff --git a/hpack/__init__.py b/hpack/__init__.py
index 7485faf..ab05c80 100644
--- a/hpack/__init__.py
+++ b/hpack/__init__.py
@@ -8,13 +8,14 @@
 from .hpack import Encoder, Decoder
 from .struct import HeaderTuple, NeverIndexedHeaderTuple
 from .exceptions import (
-    HPACKError, HPACKDecodingError, InvalidTableIndex, OversizedHeaderListError
+    HPACKError, HPACKDecodingError, InvalidTableIndex,
+    OversizedHeaderListError, ZeroLengthHeaderNameError,
 )
 
 __all__ = [
     'Encoder', 'Decoder', 'HPACKError', 'HPACKDecodingError',
     'InvalidTableIndex', 'HeaderTuple', 'NeverIndexedHeaderTuple',
-    'OversizedHeaderListError'
+    'OversizedHeaderListError', 'ZeroLengthHeaderNameError',
 ]
 
 __version__ = '3.1.0dev0'
diff --git a/hpack/exceptions.py b/hpack/exceptions.py
index 571ba98..2cdd16c 100644
--- a/hpack/exceptions.py
+++ b/hpack/exceptions.py
@@ -47,3 +47,12 @@ class InvalidTableSizeError(HPACKDecodingError):
     .. versionadded:: 3.0.0
     """
     pass
+
+
+class ZeroLengthHeaderNameError(HPACKDecodingError):
+    """
+    An invalid header with a zero length name has been received.
+
+    .. versionadded:: 3.1.0
+    """
+    pass
diff --git a/hpack/hpack.py b/hpack/hpack.py
index d5c5001..c0de505 100644
--- a/hpack/hpack.py
+++ b/hpack/hpack.py
@@ -10,7 +10,8 @@
 from .table import HeaderTable, table_entry_size
 from .compat import to_byte, to_bytes
 from .exceptions import (
-    HPACKDecodingError, OversizedHeaderListError, InvalidTableSizeError
+    HPACKDecodingError, OversizedHeaderListError, InvalidTableSizeError,
+    ZeroLengthHeaderNameError,
 )
 from .huffman import HuffmanEncoder
 from .huffman_constants import (
@@ -496,6 +497,7 @@ def decode(self, data, raw=False):
 
             if header:
                 headers.append(header)
+                self._assert_valid_header_name_size(header)
                 inflated_size += table_entry_size(*header)
 
                 if inflated_size > self.max_header_list_size:
@@ -516,6 +518,13 @@ def decode(self, data, raw=False):
         except UnicodeDecodeError:
             raise HPACKDecodingError("Unable to decode headers as UTF-8.")
 
+    def _assert_valid_header_name_size(self, header):
+        """
+        Check that the header name size is valid, i.e. non-zero.
+        """
+        if len(header[0]) == 0:
+            raise ZeroLengthHeaderNameError()
+
     def _assert_valid_table_size(self):
         """
         Check that the table size set by the encoder is lower than the maximum
diff --git a/test/test_hpack.py b/test/test_hpack.py
index c3333b4..dda19a7 100644
--- a/test/test_hpack.py
+++ b/test/test_hpack.py
@@ -2,7 +2,7 @@
 from hpack.hpack import Encoder, Decoder, _dict_to_iterable, _to_bytes
 from hpack.exceptions import (
     HPACKDecodingError, InvalidTableIndex, OversizedHeaderListError,
-    InvalidTableSizeError
+    InvalidTableSizeError, ZeroLengthHeaderNameError,
 )
 from hpack.struct import HeaderTuple, NeverIndexedHeaderTuple
 import itertools
@@ -638,6 +638,16 @@ def test_max_header_list_size(self):
         with pytest.raises(OversizedHeaderListError):
             d.decode(data)
 
+    def test_zero_length_header(self):
+        """
+        If a header has a name of zero length it is invalid and the HPACK
+        decoder raises a ZeroLengthHeaderNameError.
+        """
+        d = Decoder(max_header_list_size=44)
+        data = b"@\x80\x80"
+        with pytest.raises(ZeroLengthHeaderNameError):
+            d.decode(data)
+
     def test_can_decode_multiple_header_table_size_changes(self):
         """
         If multiple header table size changes are sent in at once, they are