diff --git a/src/librustc_mir/transform/const_prop.rs b/src/librustc_mir/transform/const_prop.rs
index a98c6721e9954..a786d3d823c8c 100644
--- a/src/librustc_mir/transform/const_prop.rs
+++ b/src/librustc_mir/transform/const_prop.rs
@@ -461,6 +461,11 @@ impl<'mir, 'tcx> ConstPropagator<'mir, 'tcx> {
     ) -> Option<()> {
         let span = source_info.span;
 
+        // #66397: Don't try to eval into large places as that can cause an OOM
+        if place_layout.size >= Size::from_bytes(MAX_ALLOC_LIMIT) {
+            return None;
+        }
+
         let overflow_check = self.tcx.sess.overflow_checks();
 
         // Perform any special handling for specific Rvalue types.
diff --git a/src/test/ui/consts/issue-66397.rs b/src/test/ui/consts/issue-66397.rs
new file mode 100644
index 0000000000000..0830c060e56af
--- /dev/null
+++ b/src/test/ui/consts/issue-66397.rs
@@ -0,0 +1,5 @@
+// build-pass
+
+fn main() {
+    [0; 4 * 1024 * 1024 * 1024 * 1024];
+}