Is the universal covering surface orientable?

Question

Let $M$ be a smooth, say also closed (compact and without boundary) surface. Is it true that its universal covering surface is orientable?

Answer 1

By definition, a universal covering surface is simply connected. Simply connected manifolds are always orientable (because a path that witnesses the non-orientabiliy can't possibly be be contractible).

Answer 2

Also, from the perspective of obstructions, the obstruction to orientability (first Stiefel-Whitney class)lives in first homology, which is zero for simply-connected spaces (trivially, Abelianizing the 0 group).