Okay, this may not be the first time this solution has been discovered, but seeing I spent many unsuccessful searches for this solution I'm proud to share it here. I was having the frustrating issue of objects or shapes not anchoring to a chart when created (Excel 2011 for Mac). Placing text boxes or shapes on a chart resulted in the objects not resizing or moving with the chart. The only anchor setting I could find was to anchor the object to the cells. I came upon the following solution through some frustrated trial and error. In your chart, layout your objects, text boxes, shapes etc. the way you want them to look. Next select all the objects and group them. Next, copy the grouped objects, select the chart, then paste the grouped objects into the chart. Finally, delete the original grouped objects and move the pasted version into place. Now, when you resize or move the chart the pasted object will move or resize as well. Bingo. Done.
Rusty