diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 3df8e0a5b..26e597ec4 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -102,6 +102,7 @@ jobs:
       - build-nix
       # - build-nix-macos
       - build-macos
+      - build-macos-xcode-27
       - build-macos-freetype
       - build-snap
       - test
@@ -1109,6 +1110,46 @@ jobs:
             COMPILATION_CACHE_CAS_PATH=/Users/runner/Library/Developer/Xcode/DerivedData/CompilationCache.noindex \
             COMPILATION_CACHE_KEEP_CAS_DIRECTORY=YES
 
+  build-macos-xcode-27:
+    runs-on: namespace-profile-ghostty-macos-tahoe
+    needs: test
+    env:
+      ZIG_LOCAL_CACHE_DIR: /Users/runner/zig/local-cache
+      ZIG_GLOBAL_CACHE_DIR: /Users/runner/zig/global-cache
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7.0.1
+
+      - name: Setup Cache
+        uses: namespacelabs/nscloud-cache-action@c5f8dab7560444c4bf8dbc64f1b203431873c547 # v1.6.1
+        with:
+          cache: |
+            xcode
+          path: |
+            /Users/runner/zig
+
+      # TODO(tahoe): https://github.com/NixOS/nix/issues/13342
+      - uses: DeterminateSystems/nix-installer-action@main
+        with:
+          determinate: true
+      - uses: cachix/cachix-action@5f2d7c5294214f71b873db4b969586b980625e71 # v17
+        with:
+          name: ghostty
+          authToken: "${{ secrets.CACHIX_AUTH_TOKEN }}"
+
+      - name: Xcode Select
+        run: sudo xcode-select -s /Applications/Xcode_27.app
+
+      - name: Xcode Version
+        run: xcodebuild -version
+
+      - name: get the Zig deps
+        id: deps
+        run: nix build -L .#deps && echo "deps=$(readlink ./result)" >> $GITHUB_OUTPUT
+
+      - name: Build with Xcode 27
+        run: nix develop -c zig build --system ${{ steps.deps.outputs.deps }} -Demit-macos-app=false
+
   build-macos-freetype:
     runs-on: namespace-profile-ghostty-macos-tahoe
     needs: test
diff --git a/pkg/apple-sdk/build.zig b/pkg/apple-sdk/build.zig
index 491e23ecf..770b36531 100644
--- a/pkg/apple-sdk/build.zig
+++ b/pkg/apple-sdk/build.zig
@@ -49,7 +49,7 @@ pub fn pathsForTarget(b: *std.Build, target: std.Target) !Cache.Value {
             // Detect our SDK using the "findNative" Zig stdlib function.
             // This is really important because it forces using `xcrun` to
             // find the SDK path.
-            const libc = std.zig.LibCInstallation.findNative(
+            var libc = std.zig.LibCInstallation.findNative(
                 b.allocator,
                 b.graph.io,
                 .{
@@ -59,6 +59,20 @@ pub fn pathsForTarget(b: *std.Build, target: std.Target) !Cache.Value {
                 },
             ) catch break :darwin;
 
+            // Xcode 27's math.h requests infinity and NaN definitions from
+            // Clang's float.h using the __need_infinity_nan protocol. Zig
+            // 0.16's bundled Clang resource headers predate that protocol, so
+            // compiling Zig's bundled libc++ against the new SDK fails.
+            //
+            // Put our compatibility include directory between Zig's resource
+            // headers and the selected SDK headers. Its math.h forwards to the
+            // SDK with #include_next, then supplies the definitions missing
+            // from Zig's float.h. This can be removed once Zig's bundled Clang
+            // headers implement __need_infinity_nan.
+            libc.include_dir = b.dependency("apple_sdk", .{})
+                .path("include")
+                .getPath(b);
+
             // Render the file compatible with the `--libc` Zig flag.
             var stream: std.Io.Writer.Allocating = .init(b.allocator);
             defer stream.deinit();
diff --git a/pkg/apple-sdk/include/math.h b/pkg/apple-sdk/include/math.h
new file mode 100644
index 000000000..507c3c707
--- /dev/null
+++ b/pkg/apple-sdk/include/math.h
@@ -0,0 +1,21 @@
+#ifndef GHOSTTY_APPLE_SDK_MATH_H
+#define GHOSTTY_APPLE_SDK_MATH_H
+
+// Resume the header search after this compatibility directory so we include
+// the selected Xcode SDK's math.h. A regular #include <math.h> would find this
+// wrapper again and loop forever. This is a Clang extension but Zig uses
+// Clang so we good.
+#include_next <math.h>
+
+// Xcode 27's math.h expects Clang's float.h to define these when requested
+// with __need_infinity_nan. Zig 0.16's bundled float.h predates that protocol;
+// remove these fallbacks once Zig's bundled Clang headers implement it.
+#ifndef INFINITY
+#define INFINITY (__builtin_inff())
+#endif
+
+#ifndef NAN
+#define NAN (__builtin_nanf(""))
+#endif
+
+#endif