diff --git a/CMakeLists.txt b/CMakeLists.txt
index 045a283fa57507daba761ecd8df4aba5f1f86d5d..4f03c39cbf01a7da920a2462f6d787fac7525a35 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -579,6 +579,7 @@ macro (CMAKE_BUILD_UTILITIES)
       set(LIBLZMA_INCLUDE_DIR
         "${CMAKE_CURRENT_SOURCE_DIR}/Utilities/cmliblzma/liblzma/api")
       set(LIBLZMA_LIBRARY cmliblzma)
+      set(HAVE_LZMA_STREAM_ENCODER_MT 1)
     endif()
   endif()
 
diff --git a/Help/cpack_gen/archive.rst b/Help/cpack_gen/archive.rst
index b9418126f829939ba19eb19eb4b0ba2244e8cee7..47e8e135466d490b9dd03378e970425c8b082822 100644
--- a/Help/cpack_gen/archive.rst
+++ b/Help/cpack_gen/archive.rst
@@ -82,7 +82,8 @@ CPack generators which are essentially archives at their core. These include:
 
   See also the :variable:`CPACK_THREADS` variable.
 
-.. note::
+  .. versionadded:: 3.21
 
-    Official CMake binaries available on ``cmake.org`` ship with a ``liblzma``
-    that does not support parallel compression.
+    Official CMake binaries available on ``cmake.org`` now ship
+    with a ``liblzma`` that supports parallel compression.
+    Older versions did not.
diff --git a/Help/release/dev/lzma-threads.rst b/Help/release/dev/lzma-threads.rst
new file mode 100644
index 0000000000000000000000000000000000000000..a481cfa684c630855a5f75c8d1f3cf638c76723b
--- /dev/null
+++ b/Help/release/dev/lzma-threads.rst
@@ -0,0 +1,7 @@
+lzma-threads
+------------
+
+* The precompiled binaries provided on
+  `cmake.org <https://cmake.org/download/>`_ now support
+  ``liblzma`` multi-threading.  See the :variable:`CPACK_THREADS` and
+  :variable:`CPACK_ARCHIVE_THREADS` variables.
diff --git a/Modules/CPack.cmake b/Modules/CPack.cmake
index ef5a7d5b1a92ccfa89f2ac594cf6dd761c1dd2f9..3b29ede644d3028912c7d668bfe566eb97671589 100644
--- a/Modules/CPack.cmake
+++ b/Modules/CPack.cmake
@@ -299,10 +299,11 @@ installers.  The most commonly-used variables are:
   Currently only ``xz`` compression *may* take advantage of multiple cores. Other
   compression methods ignore this value and use only one thread.
 
-  .. note::
+  .. versionadded:: 3.21
 
-     Official CMake binaries available on ``cmake.org`` ship with a ``liblzma``
-     that does not support parallel compression.
+    Official CMake binaries available on ``cmake.org`` now ship
+    with a ``liblzma`` that supports parallel compression.
+    Older versions did not.
 
 Variables for Source Package Generators
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
diff --git a/Utilities/cmliblzma/CMakeLists.txt b/Utilities/cmliblzma/CMakeLists.txt
index 5dd7035da3c795a51be026bd91392c9612e65993..4820a8fd01f4408be6b7620d9122d42692ab7139 100644
--- a/Utilities/cmliblzma/CMakeLists.txt
+++ b/Utilities/cmliblzma/CMakeLists.txt
@@ -6,6 +6,12 @@ include(CheckSymbolExists)
 include(CheckTypeSize)
 include(TestBigEndian)
 
+if(WIN32)
+  add_definitions(-DMYTHREAD_VISTA)
+else()
+  add_definitions(-DMYTHREAD_POSIX)
+endif()
+
 CHECK_INCLUDE_FILE(byteswap.h HAVE_BYTESWAP_H)
 CHECK_INCLUDE_FILE(limits.h HAVE_LIMITS_H)
 CHECK_INCLUDE_FILE(memory.h HAVE_MEMORY_H)
@@ -60,7 +66,10 @@ set(HAVE_MF_HC3 1)
 set(HAVE_MF_HC4 1)
 
 SET(LZMA_SRCS
+  common/mythread.h
   common/sysdefs.h
+  common/tuklib_cpucores.c
+  common/tuklib_cpucores.h
   common/tuklib_integer.h
   liblzma/check/check.c
   liblzma/check/crc32_fast.c
@@ -91,14 +100,17 @@ SET(LZMA_SRCS
   liblzma/common/filter_encoder.c
   liblzma/common/filter_flags_decoder.c
   liblzma/common/filter_flags_encoder.c
+  liblzma/common/hardware_cputhreads.c
   liblzma/common/index.c
   liblzma/common/index_decoder.c
   liblzma/common/index_encoder.c
   liblzma/common/index_hash.c
+  liblzma/common/outqueue.c
   liblzma/common/stream_buffer_decoder.c
   liblzma/common/stream_buffer_encoder.c
   liblzma/common/stream_decoder.c
   liblzma/common/stream_encoder.c
+  liblzma/common/stream_encoder_mt.c
   liblzma/common/stream_flags_common.c
   liblzma/common/stream_flags_decoder.c
   liblzma/common/stream_flags_encoder.c
diff --git a/Utilities/cmliblzma/liblzma/common/common.h b/Utilities/cmliblzma/liblzma/common/common.h
index dde3ae0eca4b7300a36e32dda38ecba177008ce4..b3d3b7a059b108592e23232c6b92779000d41d18 100644
--- a/Utilities/cmliblzma/liblzma/common/common.h
+++ b/Utilities/cmliblzma/liblzma/common/common.h
@@ -14,6 +14,7 @@
 #define LZMA_COMMON_H
 
 #include "sysdefs.h"
+#include "mythread.h"
 #include "tuklib_integer.h"
 
 #if defined(_WIN32) || defined(__CYGWIN__)