diff --git a/changes/ticket40511 b/changes/ticket40511
new file mode 100644
index 0000000000..756edd874d
--- /dev/null
+++ b/changes/ticket40511
@@ -0,0 +1,6 @@
+  o Minor features (compilation):
+    - Give an error message if trying to build with a version of LibreSSL
+      known not to work with Tor.  (There's an incompatibility with
+      LibreSSL versions 3.2.1 through 3.4.0 inclusive because of their
+      incompatibility with OpenSSL 1.1.1's TLSv1.3 APIs.)
+      Closes ticket 40511.
diff --git a/configure.ac b/configure.ac
index 249a250a2f..8ab35bf9dd 100644
--- a/configure.ac
+++ b/configure.ac
@@ -963,6 +963,18 @@ AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
    [ AC_MSG_RESULT([no]) ],
    [ AC_MSG_ERROR([OpenSSL is too old. We require 1.0.1 or later. You can specify a path to a newer one with --with-openssl-dir.]) ])
 
+AC_MSG_CHECKING([whether LibreSSL TLS 1.3 APIs are busted])
+AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
+#include <openssl/opensslv.h>
+#if defined(LIBRESSL_VERSION_NUMBER) && \
+     LIBRESSL_VERSION_NUMBER >= 0x3020100fL && \
+     LIBRESSL_VERSION_NUMBER < 0x3040100fL
+#error "oh no"
+#endif
+   ]], [[]])],
+   [ AC_MSG_RESULT([no]) ],
+   [ AC_MSG_ERROR([This version of LibreSSL won't work with Tor. Please upgrade to LibreSSL 3.4.1 or later. (Or downgrade to 3.2.0 if you really must.)]) ])
+
 AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[
 #include <openssl/opensslv.h>
 #include <openssl/evp.h>