Are there any simply connected parallelizable 4-manifolds?

On pp. 166 of Scorpan's "The Wild World of 4--manifolds", he gives an example of a parallelizable 4-manifold ($S^1\times S^3$) and then asserts: "there are no simply connected examples". It's confusing to me whether he means that there are no such examples in general, or examples that are 4-manifolds. In any case, here is my question:

Do there exist (compact, smooth, oriented) simply connected manifolds that are parallelizable? 4-manifolds?

(Recall that a manifold is called parallelizable if it has a trivial tangent bundle.)

A simply connected smooth compact 4-manifold has its homology concentrated in even degrees, by Poincare duality. Thus its Euler characteristic is positive. By the Poincare-Hopf index theorem, such a manifold can have no nowhere vanishing vector field, and so is certainly not parallelizable.

At least $S^3$ is a lie group so parallelizable.