diff --git a/build_utils/build_libomp.sh b/build_utils/build_libomp.sh
index fd25797..0912585 100644
--- a/build_utils/build_libomp.sh
+++ b/build_utils/build_libomp.sh
@@ -2,16 +2,18 @@
 set -euo pipefail
 DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" >/dev/null 2>&1 && pwd )"
 build_dir=${DIR}/libs_build
-LLVM_VERSION=${LLVM_VERSION:-19.1.1}
+LLVM_VERSION=${LLVM_VERSION:-23.1.2}
 INSTALL_CMD=${INSTALL_CMD:-"sudo make install"}
 
-echo MACOSX_DEPLOYMENT_TARGET $MACOSX_DEPLOYMENT_TARGET
+echo MACOSX_DEPLOYMENT_TARGET ${MACOSX_DEPLOYMENT_TARGET:-}
 
 git clone --depth 1 --branch llvmorg-${LLVM_VERSION} https://github.com/llvm/llvm-project
-pushd llvm-project/openmp
+pushd llvm-project
+# The legacy standalone build (cmake llvm-project/openmp) was removed in LLVM 23,
+# openmp has to be built through the runtimes directory.
 mkdir build
 cd build
-cmake -DCMAKE_C_COMPILER=${CC:-clang} -DCMAKE_CXX_COMPILER=${CXX:-clang++} ${CMAKE_FLAGS:-} ..
+cmake -DCMAKE_C_COMPILER=${CC:-clang} -DCMAKE_CXX_COMPILER=${CXX:-clang++} -DLLVM_ENABLE_RUNTIMES=openmp ${CMAKE_FLAGS:-} ../runtimes
 make ${MAKE_FLAGS:-}
 ${INSTALL_CMD}
 
diff --git a/pyproject.toml b/pyproject.toml
index 52e1b96..ae19bf4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -133,6 +133,8 @@ build = "*64"
 enable = ["pypy"]
 
 [tool.cibuildwheel.macos]
+# libomp (LLVM 23) uses aligned_alloc, available since macOS 10.15
+environment = { MACOSX_DEPLOYMENT_TARGET = "10.15" }
 before-all = [
     "set",
     "bash {project}/build_utils/build_libomp.sh",