diff --git a/lldb/CMakeLists.txt b/lldb/CMakeLists.txt
--- a/lldb/CMakeLists.txt
+++ b/lldb/CMakeLists.txt
@@ -37,18 +37,29 @@
           -c "import distutils.sysconfig; print(distutils.sysconfig.get_python_lib(True, False, ''))"
       OUTPUT_VARIABLE LLDB_PYTHON_DEFAULT_RELATIVE_PATH
       OUTPUT_STRIP_TRAILING_WHITESPACE)
-
     file(TO_CMAKE_PATH ${LLDB_PYTHON_DEFAULT_RELATIVE_PATH} LLDB_PYTHON_DEFAULT_RELATIVE_PATH)
+    execute_process(
+      COMMAND ${Python3_EXECUTABLE}
+          -c "import sysconfig; print(sysconfig.get_config_var('EXT_SUFFIX'))"
+      OUTPUT_VARIABLE LLDB_PYTHON_DEFAULT_EXT_SUFFIX
+      OUTPUT_STRIP_TRAILING_WHITESPACE)
   else ()
     if ("${LLDB_PYTHON_RELATIVE_PATH}" STREQUAL "")
       message(FATAL_ERROR
         "Crosscompiling LLDB with Python requires manually setting
         LLDB_PYTHON_RELATIVE_PATH.")
     endif ()
+    if ("${LLDB_PYTHON_EXT_SUFFIX}" STREQUAL "")
+      message(FATAL_ERROR
+        "Crosscompiling LLDB with Python requires manually setting
+        LLDB_PYTHON_EXT_SUFFIX.")
+    endif ()
   endif ()
 
   set(LLDB_PYTHON_RELATIVE_PATH ${LLDB_PYTHON_DEFAULT_RELATIVE_PATH}
-    CACHE STRING "Path where Python modules are installed, relative to install prefix")
+    CACHE STRING "Path where Python modules are installed, relative to install prefix.")
+  set(LLDB_PYTHON_EXT_SUFFIX ${LLDB_PYTHON_DEFAULT_EXT_SUFFIX}
+    CACHE STRING "Filename suffix for Python modules.")
 endif ()
 
 if (LLDB_ENABLE_LUA)
diff --git a/lldb/bindings/python/CMakeLists.txt b/lldb/bindings/python/CMakeLists.txt
--- a/lldb/bindings/python/CMakeLists.txt
+++ b/lldb/bindings/python/CMakeLists.txt
@@ -138,13 +138,14 @@
     set(LIBLLDB_SYMLINK_DEST "${LLVM_SHLIB_OUTPUT_INTDIR}/liblldb${CMAKE_SHARED_LIBRARY_SUFFIX}")
   endif()
   if(WIN32)
+    # FIXME should we use EXT_SUFFIX on windows?
     if(CMAKE_BUILD_TYPE STREQUAL Debug)
       set(LIBLLDB_SYMLINK_OUTPUT_FILE "_lldb_d.pyd")
     else()
       set(LIBLLDB_SYMLINK_OUTPUT_FILE "_lldb.pyd")
     endif()
   else()
-    set(LIBLLDB_SYMLINK_OUTPUT_FILE "_lldb.so")
+    set(LIBLLDB_SYMLINK_OUTPUT_FILE "_lldb${LLDB_PYTHON_EXT_SUFFIX}")
   endif()
   create_relative_symlink(${swig_target} ${LIBLLDB_SYMLINK_DEST}
                           ${lldb_python_target_dir} ${LIBLLDB_SYMLINK_OUTPUT_FILE})