diff --git a/.travis.yml b/.travis.yml
new file mode 100644
index 00000000..d269ab07
--- /dev/null
+++ b/.travis.yml
@@ -0,0 +1,8 @@
+language: cpp
+compiler:
+  - gcc
+  - clang
+script: ./install.sh
+env:
+  - YCM_TESTRUN=1 EXTRA_CMAKE_ARGS=""
+  - YCM_TESTRUN=1 EXTRA_CMAKE_ARGS="-DUSE_CLANG_COMPLETER=ON"
diff --git a/cpp/CMakeLists.txt b/cpp/CMakeLists.txt
index 909f8de1..ed2a362c 100644
--- a/cpp/CMakeLists.txt
+++ b/cpp/CMakeLists.txt
@@ -41,7 +41,11 @@ endif()
 
 if ( CMAKE_CXX_COMPILER_ID STREQUAL "Clang" )
   set( COMPILER_IS_CLANG true )
-  set( CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -stdlib=libc++" )
+
+  # The Travis CI build machines don't have libc++ installed
+  if ( NOT DEFINED ENV{TRAVIS} )
+    set( CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -stdlib=libc++" )
+  endif()
 endif()
 
 if ( CMAKE_GENERATOR STREQUAL Xcode )
diff --git a/install.sh b/install.sh
index b499d94c..81730d6d 100755
--- a/install.sh
+++ b/install.sh
@@ -82,6 +82,20 @@ function install {
   rm -rf $build_dir
 }
 
+function testrun {
+  ycm_dir=`pwd`
+  build_dir=`mktemp -d -t ycm_build.XXXXXX`
+  pushd $build_dir
+
+  cmake -G "Unix Makefiles" $1 . $ycm_dir/cpp
+  make -j $(num_cores) ycm_core_tests
+  cd ycm/tests
+  LD_LIBRARY_PATH=$ycm_dir/python ./ycm_core_tests
+
+  popd
+  rm -rf $build_dir
+}
+
 function linux_cmake_install {
   echo "Please install CMake using your package manager and retry."
   exit 1
@@ -112,4 +126,10 @@ if ! command_exists cmake; then
   echo "CMake is required to build YouCompleteMe."
   cmake_install
 fi
-install $cmake_args
+
+if [ -z "$YCM_TESTRUN" ]; then
+  install $cmake_args $EXTRA_CMAKE_ARGS
+else
+  testrun $cmake_args $EXTRA_CMAKE_ARGS
+fi
+