diff --git a/CMakeLists.txt b/CMakeLists.txt
index f8eeebd3..b214d71d 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -9,7 +9,6 @@
 #
 # On some platforms this builds also xz and xzdec, but these are
 # highly experimental and meant for testing only:
-#   - No large file support on those 32-bit platforms that need it
 #   - No replacement getopt_long(), libc must have it
 #   - No sandboxing support
 #   - No translations
@@ -53,6 +52,7 @@ include(CheckIncludeFile)
 include(CheckSymbolExists)
 include(CheckStructHasMember)
 include(CheckCSourceCompiles)
+include(cmake/tuklib_large_file_support.cmake)
 include(cmake/tuklib_integer.cmake)
 include(cmake/tuklib_cpucores.cmake)
 include(cmake/tuklib_physmem.cmake)
@@ -152,6 +152,11 @@ add_compile_definitions(
 # it also adds the definitions to CMAKE_REQUIRED_DEFINITIONS.
 tuklib_use_system_extensions(ALL)
 
+# Check for large file support. It's required on some 32-bit platforms and
+# even on 64-bit MinGW-w64 to get 64-bit off_t. This can be forced off on
+# the CMake command line if needed: -DLARGE_FILE_SUPPORT=OFF
+tuklib_large_file_support(ALL)
+
 # This is needed by liblzma and xz.
 tuklib_integer(ALL)
 
diff --git a/cmake/tuklib_large_file_support.cmake b/cmake/tuklib_large_file_support.cmake
new file mode 100644
index 00000000..0800faa2
--- /dev/null
+++ b/cmake/tuklib_large_file_support.cmake
@@ -0,0 +1,52 @@
+#
+# tuklib_large_file_support.cmake
+#
+# If off_t is less than 64 bits by default and -D_FILE_OFFSET_BITS=64
+# makes off_t become 64-bit, the CMake option LARGE_FILE_SUPPORT is
+# provided (ON by default) and -D_FILE_OFFSET_BITS=64 is added to
+# the compile definitions if LARGE_FILE_SUPPORT is ON.
+#
+# Author: Lasse Collin
+#
+# This file has been put into the public domain.
+# You can do whatever you want with this file.
+#
+
+include("${CMAKE_CURRENT_LIST_DIR}/tuklib_common.cmake")
+include(CheckCSourceCompiles)
+
+function(tuklib_large_file_support TARGET_OR_ALL)
+    # MSVC must be handled specially in the C code.
+    if(MSVC)
+        return()
+    endif()
+
+    set(TUKLIB_LARGE_FILE_SUPPORT_TEST
+            "#include <sys/types.h>
+            int foo[sizeof(off_t) >= 8 ? 1 : -1];
+            int main(void) { return 0; }")
+
+    check_c_source_compiles("${TUKLIB_LARGE_FILE_SUPPORT_TEST}"
+                            TUKLIB_LARGE_FILE_SUPPORT_BY_DEFAULT)
+
+    if(NOT TUKLIB_LARGE_FILE_SUPPORT_BY_DEFAULT)
+        cmake_push_check_state()
+        # This needs -D.
+        list(APPEND CMAKE_REQUIRED_DEFINITIONS "-D_FILE_OFFSET_BITS=64")
+        check_c_source_compiles("${TUKLIB_LARGE_FILE_SUPPORT_TEST}"
+                                TUKLIB_LARGE_FILE_SUPPORT_WITH_FOB64)
+        cmake_pop_check_state()
+    endif()
+
+    if(TUKLIB_LARGE_FILE_SUPPORT_WITH_FOB64)
+        # Show the option only when _FILE_OFFSET_BITS=64 affects sizeof(off_t).
+        option(LARGE_FILE_SUPPORT
+               "Use -D_FILE_OFFSET_BITS=64 to support files larger than 2 GiB."
+               ON)
+
+        if(LARGE_FILE_SUPPORT)
+            # This must not use -D.
+            tuklib_add_definitions("${TARGET_OR_ALL}" "_FILE_OFFSET_BITS=64")
+        endif()
+    endif()
+endfunction()