The following code works fine:
class Test {
	int x;
	Test() {}
	Test.with_x(int x) { this.x=x; this(); }
	static int main() { var test = new Test.with_x(2); return 0; }
}

However, the following code gives a segmentation fault:
class Test {
	int x; int y;
	Test() { y=3; }
	Test.with_x(int x) { this.x=x; this(); }
	static int main() { var test = new Test.with_x(2); return 0; }
}

The reason can be found in the C code:
static Test* test_construct_with_x (GType object_type, gint x) {
        Test* self;
        self->priv->x = x;
        self = (Test*) test_construct (object_type);
        return self;
}

So, "self" is accessed before it is initialized.

I believe that either:
(1) self should be initialized; then the .with_x constructor code executed; then the basic constructor code.
OR
(2) valac should emit an error message in this case