diff --git a/t/t5000-tar-tree.sh b/t/t5000-tar-tree.sh
index 4b68bbafbe..950bdd31e7 100755
--- a/t/t5000-tar-tree.sh
+++ b/t/t5000-tar-tree.sh
@@ -319,4 +319,78 @@ test_expect_success 'catch non-matching pathspec' '
 	test_must_fail git archive -v HEAD -- "*.abc" >/dev/null
 '
 
+# Pull the size and date of each entry in a tarfile using the system tar.
+#
+# We'll pull out only the year from the date; that avoids any question of
+# timezones impacting the result (as long as we keep our test times away from a
+# year boundary; our reference times are all in August).
+#
+# The output of tar_info is expected to be "<size> <year>", both in decimal. It
+# ignores the return value of tar. We have to do this, because some of our test
+# input is only partial (the real data is 64GB in some cases).
+tar_info () {
+	"$TAR" tvf "$1" |
+	awk '{
+		split($4, date, "-")
+		print $3 " " date[1]
+	}'
+}
+
+# See if our system tar can handle a tar file with huge sizes and dates far in
+# the future, and that we can actually parse its output.
+#
+# The reference file was generated by GNU tar, and the magic time and size are
+# both octal 01000000000001, which overflows normal ustar fields.
+test_lazy_prereq TAR_HUGE '
+	echo "68719476737 4147" >expect &&
+	tar_info "$TEST_DIRECTORY"/t5000/huge-and-future.tar >actual &&
+	test_cmp expect actual
+'
+
+test_expect_success 'set up repository with huge blob' '
+	obj_d=19 &&
+	obj_f=f9c8273ec45a8938e6999cb59b3ff66739902a &&
+	obj=${obj_d}${obj_f} &&
+	mkdir -p .git/objects/$obj_d &&
+	cp "$TEST_DIRECTORY"/t5000/$obj .git/objects/$obj_d/$obj_f &&
+	rm -f .git/index &&
+	git update-index --add --cacheinfo 100644,$obj,huge &&
+	git commit -m huge
+'
+
+# We expect git to die with SIGPIPE here (otherwise we
+# would generate the whole 64GB).
+test_expect_failure 'generate tar with huge size' '
+	{
+		git archive HEAD
+		echo $? >exit-code
+	} | test_copy_bytes 4096 >huge.tar &&
+	echo 141 >expect &&
+	test_cmp expect exit-code
+'
+
+test_expect_failure TAR_HUGE 'system tar can read our huge size' '
+	echo 68719476737 >expect &&
+	tar_info huge.tar | cut -d" " -f1 >actual &&
+	test_cmp expect actual
+'
+
+test_expect_success 'set up repository with far-future commit' '
+	rm -f .git/index &&
+	echo content >file &&
+	git add file &&
+	GIT_COMMITTER_DATE="@68719476737 +0000" \
+		git commit -m "tempori parendum"
+'
+
+test_expect_failure 'generate tar with future mtime' '
+	git archive HEAD >future.tar
+'
+
+test_expect_failure TAR_HUGE 'system tar can read our future mtime' '
+	echo 4147 >expect &&
+	tar_info future.tar | cut -d" " -f2 >actual &&
+	test_cmp expect actual
+'
+
 test_done
diff --git a/t/t5000/19f9c8273ec45a8938e6999cb59b3ff66739902a b/t/t5000/19f9c8273ec45a8938e6999cb59b3ff66739902a
new file mode 100644
index 0000000000..5cbe9ec312
Binary files /dev/null and b/t/t5000/19f9c8273ec45a8938e6999cb59b3ff66739902a differ
diff --git a/t/t5000/huge-and-future.tar b/t/t5000/huge-and-future.tar
new file mode 100644
index 0000000000..63155e1855
Binary files /dev/null and b/t/t5000/huge-and-future.tar differ