Let
![$X$](img28.png)
be an abelian surface. It is a recent result due to
Beauville that all polarized abelian surfaces possess an Ulrich
(hence ACM) bundle of rank
![$2$](img29.png)
. However, the case of ACM line
bundles was left open. In this note we solve the problem in the
affirmative by discussing their existence on a member of the isogeny
class of any
![$X$](img28.png)
in the case of Picard number
![$4$](img30.png)
, and finally
extend to any such
![$X$](img28.png)
.