In the interests of accuracy - it's not a chute. Rather, it's a rather broad snowfield, especially at this time of year. It's at least a hundred yards wide - that's not a chute. It can be icy in places, especially early/late in the day, when the sun isn't on it.
Having said that - I would agree with what others have said re: crampons and ice axe.
Note (edit) - whether an axe or crampons are more important is a personal matter. For me, crampons are far more important. Much better to prevent a slip/fall before it occurs, rather with the fall itself. Knowing how to use an ice axe by NO means guarantees that you will be able to stop.
Here's a pic Tracie posted on the WPSBB: