Index: clang/include/clang/Driver/Multilib.h
===================================================================
--- clang/include/clang/Driver/Multilib.h
+++ clang/include/clang/Driver/Multilib.h
@@ -34,10 +34,11 @@
   std::string OSSuffix;
   std::string IncludeSuffix;
   flags_list Flags;
+  int Priority;
 
 public:
   Multilib(StringRef GCCSuffix = {}, StringRef OSSuffix = {},
-           StringRef IncludeSuffix = {});
+           StringRef IncludeSuffix = {}, int Priority = 0);
 
   /// Get the detected GCC installation path suffix for the multi-arch
   /// target variant. Always starts with a '/', unless empty
@@ -77,6 +78,10 @@
   const flags_list &flags() const { return Flags; }
   flags_list &flags() { return Flags; }
 
+  /// Returns the multilib priority. When more than one multilib matches flags,
+  /// the one with the highest priority is selected, with 0 being the default.
+  int priority() const { return Priority; }
+
   /// Add a flag to the flags list
   /// \p Flag must be a flag accepted by the driver with its leading '-' removed,
   ///     and replaced with either:
Index: clang/lib/Driver/Multilib.cpp
===================================================================
--- clang/lib/Driver/Multilib.cpp
+++ clang/lib/Driver/Multilib.cpp
@@ -51,8 +51,9 @@
 }
 
 Multilib::Multilib(StringRef GCCSuffix, StringRef OSSuffix,
-                   StringRef IncludeSuffix)
-    : GCCSuffix(GCCSuffix), OSSuffix(OSSuffix), IncludeSuffix(IncludeSuffix) {
+                   StringRef IncludeSuffix, int Priority)
+    : GCCSuffix(GCCSuffix), OSSuffix(OSSuffix), IncludeSuffix(IncludeSuffix),
+      Priority(Priority) {
   normalizePathSegment(this->GCCSuffix);
   normalizePathSegment(this->OSSuffix);
   normalizePathSegment(this->IncludeSuffix);
@@ -265,8 +266,19 @@
     return true;
   }
 
-  // TODO: pick the "best" multlib when more than one is suitable
-  assert(false);
+  // Sort multilibs by priority and select the one with the highest priority.
+  llvm::sort(Filtered.begin(), Filtered.end(),
+             [](const Multilib &a, const Multilib &b) -> bool {
+               return a.priority() > b.priority();
+             });
+
+  if (Filtered[0].priority() > Filtered[1].priority()) {
+    M = Filtered[0];
+    return true;
+  }
+
+  // TODO: We should consider returning llvm::Error rather than aborting.
+  assert(false && "More than one multilib with the same priority");
   return false;
 }
 
Index: clang/unittests/Driver/MultilibTest.cpp
===================================================================
--- clang/unittests/Driver/MultilibTest.cpp
+++ clang/unittests/Driver/MultilibTest.cpp
@@ -349,3 +349,27 @@
   Latte.combineWith(Milk);
   ASSERT_EQ(Latte.size(), (unsigned)2);
 }
+
+TEST(MultilibTest, SetPriority) {
+  MultilibSet MS;
+  MS.push_back(Multilib("noexcept", {}, {}, 1).flag("+fno-exceptions"));
+  MS.push_back(Multilib("asan", {}, {}, 2).flag("+fsanitize=address"));
+
+  Multilib::flags_list Flags1;
+  Flags1.push_back("+fno-exceptions");
+  Flags1.push_back("-fsanitize=address");
+  Multilib SelectionNoExcept;
+  ASSERT_TRUE(MS.select(Flags1, SelectionNoExcept))
+      << "Flag set was {\"+fno-exceptions\"}, but selection not found";
+  ASSERT_TRUE(SelectionNoExcept.gccSuffix() == "/noexcept")
+      << "Selection picked " << SelectionNoExcept << " which was not expected";
+
+  Multilib::flags_list Flags2;
+  Flags2.push_back("+fno-exceptions");
+  Flags2.push_back("+fsanitize=address");
+  Multilib SelectionASan;
+  ASSERT_TRUE(MS.select(Flags2, SelectionASan))
+      << "Flag set was {\"+fsanitize=address\"}, but selection not found";
+  ASSERT_TRUE(SelectionASan.gccSuffix() == "/asan")
+      << "Selection picked " << SelectionASan << " which was not expected";
+}