diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index a2da758..5cfb683 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -11,7 +11,8 @@
 Backward-incompatible changes:
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-*none*
+- ``X509Store.add_cert`` no longer raises an error if you add a duplicate cert.
+  `#787 <https://github.com/pyca/pyopenssl/pull/787>`_
 
 
 Deprecations:
diff --git a/src/OpenSSL/crypto.py b/src/OpenSSL/crypto.py
index d40f23c..ea7b354 100644
--- a/src/OpenSSL/crypto.py
+++ b/src/OpenSSL/crypto.py
@@ -1607,7 +1607,16 @@
         if not isinstance(cert, X509):
             raise TypeError()
 
-        _openssl_assert(_lib.X509_STORE_add_cert(self._store, cert._x509) != 0)
+        # As of OpenSSL 1.1.0i adding the same cert to the store more than
+        # once doesn't cause an error. Accordingly, this code now silences
+        # the error for OpenSSL < 1.1.0i as well.
+        if _lib.X509_STORE_add_cert(self._store, cert._x509) == 0:
+            code = _lib.ERR_peek_error()
+            err_reason = _lib.ERR_GET_REASON(code)
+            _openssl_assert(
+                err_reason == _lib.X509_R_CERT_ALREADY_IN_HASH_TABLE
+            )
+            _lib.ERR_clear_error()
 
     def add_crl(self, crl):
         """
diff --git a/tests/test_crypto.py b/tests/test_crypto.py
index d1c261b..eb4590d 100644
--- a/tests/test_crypto.py
+++ b/tests/test_crypto.py
@@ -2016,16 +2016,15 @@
         with pytest.raises(TypeError):
             store.add_cert(cert)
 
-    def test_add_cert_rejects_duplicate(self):
+    def test_add_cert_accepts_duplicate(self):
         """
-        `X509Store.add_cert` raises `OpenSSL.crypto.Error` if an attempt is
-        made to add the same certificate to the store more than once.
+        `X509Store.add_cert` doesn't raise `OpenSSL.crypto.Error` if an attempt
+        is made to add the same certificate to the store more than once.
         """
         cert = load_certificate(FILETYPE_PEM, cleartextCertificatePEM)
         store = X509Store()
         store.add_cert(cert)
-        with pytest.raises(Error):
-            store.add_cert(cert)
+        store.add_cert(cert)
 
 
 class TestPKCS12(object):