diff --git a/libcxx/include/string_view b/libcxx/include/string_view
--- a/libcxx/include/string_view
+++ b/libcxx/include/string_view
@@ -331,7 +331,7 @@
     size_type length()   const _NOEXCEPT { return __size; }
 
     _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
-    size_type max_size() const _NOEXCEPT { return numeric_limits<size_type>::max(); }
+    size_type max_size() const _NOEXCEPT { return (numeric_limits<size_type>::max() - sizeof(*this)) / sizeof(value_type); }
 
     _LIBCPP_NODISCARD_AFTER_CXX17 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR
     bool empty()         const _NOEXCEPT { return __size == 0; }
diff --git a/libcxx/test/std/strings/string.view/string.view.capacity/capacity.pass.cpp b/libcxx/test/std/strings/string.view/string.view.capacity/capacity.pass.cpp
--- a/libcxx/test/std/strings/string.view/string.view.capacity/capacity.pass.cpp
+++ b/libcxx/test/std/strings/string.view/string.view.capacity/capacity.pass.cpp
@@ -16,6 +16,7 @@
 
 #include <string_view>
 #include <cassert>
+#include <limits>
 
 #include "test_macros.h"
 
@@ -42,6 +43,18 @@
     assert ( sv1.size() == sv1.length());
     assert ( sv1.max_size() > sv1.size());
     }
+
+    // Sanity check max_size(). It has to be smaller than numeric_limits<size_type>::max(),
+    // because representing std::string_view requires _at least_ one byte. In reality it
+    // needs a lot more than that, however any implementation that fails this check probably
+    // has a bug.
+    {
+        typedef typename SV::value_type CharT;
+        typedef typename SV::size_type Size;
+        SV sv;
+        assert(sv.max_size() < std::numeric_limits<Size>::max());
+        LIBCPP_ASSERT(sv.max_size() == (std::numeric_limits<Size>::max() - sizeof(SV)) / sizeof(CharT));
+    }
 }
 
 template<typename CharT>