diff --git a/sdk/core/azure-core/src/http/curl/curl.cpp b/sdk/core/azure-core/src/http/curl/curl.cpp
index 121de00ad..9b78dced2 100644
--- a/sdk/core/azure-core/src/http/curl/curl.cpp
+++ b/sdk/core/azure-core/src/http/curl/curl.cpp
@@ -446,7 +446,18 @@ void CurlSession::ParseChunkSize(Context const& context)
       if (i > 1 && this->m_readBuffer[index] == '\n')
       {
         // get chunk size. Chunk size comes in Hex value
-        this->m_chunkSize = static_cast<int64_t>(std::stoull(strChunkSize, nullptr, 16));
+        try
+        {
+          this->m_chunkSize = static_cast<int64_t>(std::stoull(strChunkSize, nullptr, 16));
+        }
+        catch (std::invalid_argument& err)
+        {
+          (void)err;
+          // Server can return something like `\n\r\n` for a chunk of zero length data. This is
+          // allowed by RFC. `stoull` will throw invalid_argument if there is not at least one hex
+          // digit to be parsed. For those cases, we consider the response as zero-lenght.
+          this->m_chunkSize = 0;
+        }
 
         if (this->m_chunkSize == 0)
         { // Response with no content. end of chunk
diff --git a/sdk/core/azure-core/test/ut/curl_session.hpp b/sdk/core/azure-core/test/ut/curl_session.hpp
index 1e11b1611..9911d31e6 100644
--- a/sdk/core/azure-core/test/ut/curl_session.hpp
+++ b/sdk/core/azure-core/test/ut/curl_session.hpp
@@ -3,10 +3,10 @@
 
 /**
  * @file
- * @brief The base class for testing a curl session. 
- * 
+ * @brief The base class for testing a curl session.
+ *
  * @remark The curl connection mock is defined here.
- * 
+ *
  */
 
 #include <gmock/gmock.h>
@@ -39,6 +39,12 @@ namespace Azure { namespace Core { namespace Test {
         SendBuffer,
         (Context const& context, uint8_t const* buffer, size_t bufferSize),
         (override));
+
+    /* This is a way to test we are calling the destructor
+     *  Adding an extra mock method that is called from the destructor
+     */
+    MOCK_METHOD(void, DestructObj, ());
+    virtual ~MockCurlNetworkConnection() { DestructObj(); }
   };
 
 }}} // namespace Azure::Core::Test
diff --git a/sdk/core/azure-core/test/ut/curl_session_test.cpp b/sdk/core/azure-core/test/ut/curl_session_test.cpp
index b6abf1bfb..46e218f4b 100644
--- a/sdk/core/azure-core/test/ut/curl_session_test.cpp
+++ b/sdk/core/azure-core/test/ut/curl_session_test.cpp
@@ -9,6 +9,7 @@
 using ::testing::_;
 using ::testing::DoAll;
 using ::testing::Return;
+using ::testing::ReturnRef;
 using ::testing::SetArrayArgument;
 
 namespace Azure { namespace Core { namespace Test {
@@ -41,4 +42,40 @@ namespace Azure { namespace Core { namespace Test {
 
     EXPECT_NO_THROW(session->Perform(Azure::Core::GetApplicationContext()));
   }
+
+  TEST_F(CurlSession, chunkResponseSizeZero)
+  {
+    // chunked response with no content and no size
+    std::string response("HTTP/1.1 200 Ok\r\ntransfer-encoding: chunked\r\n\r\n\n\r\n");
+    std::string host("sample-host");
+
+    // Can't mock the curMock directly from a unique ptr, heap allocate it first and then make a
+    // unique ptr for it
+    MockCurlNetworkConnection* curlMock = new MockCurlNetworkConnection();
+    EXPECT_CALL(*curlMock, SendBuffer(_, _, _)).WillOnce(Return(CURLE_OK));
+    EXPECT_CALL(*curlMock, ReadFromSocket(_, _, _))
+        .WillOnce(DoAll(
+            SetArrayArgument<1>(response.data(), response.data() + response.size()),
+            Return(response.size())));
+    EXPECT_CALL(*curlMock, GetHost()).WillRepeatedly(ReturnRef(host));
+    EXPECT_CALL(*curlMock, updateLastUsageTime());
+    EXPECT_CALL(*curlMock, DestructObj());
+
+    // Create the unique ptr to take care about memory free at the end
+    std::unique_ptr<MockCurlNetworkConnection> uniqueCurlMock(curlMock);
+
+    // Simulate a request to be sent
+    Azure::Core::Http::Url url("http://microsoft.com");
+    Azure::Core::Http::Request request(Azure::Core::Http::HttpMethod::Get, url);
+
+    {
+      // Create the session inside scope so it is released and the connection is moved to the pool
+      auto session
+          = std::make_unique<Azure::Core::Http::CurlSession>(request, std::move(uniqueCurlMock));
+
+      EXPECT_NO_THROW(session->Perform(Azure::Core::GetApplicationContext()));
+    }
+    // Clear the connections from the pool to invoke clean routine
+    Azure::Core::Http::CurlConnectionPool::ConnectionPoolIndex.clear();
+  }
 }}} // namespace Azure::Core::Test