Thanks, Rohit. Well, no, ChartLabels and friends do not seem to work in this case. I only could make it in this clumsy way (notice the "\n" in the first framelabel):

data = {{80, 20, 25, 15}, {40, 60, 30, 20}, {10, 55, 20, 50}, {0, 40, 
     10, 50}, {0, 25, 10, 75}, {0, 10, 0, 100}, {0, 0, 0, 120}} /. 0 -> _;
bch = BarChart[data, ChartLayout -> "Stacked", Axes -> True, 
   Frame -> True, 
   FrameLabel -> {"\nFood Age {days}", "Consumption {calories}"}, 
   PlotLabel -> "Food Consumption by Age", 
   ChartLegends -> {"Fresh kill", "Canned food", "Kitchen scraps", 
     "Dry food"}, LabelingFunction -> Center, ImageSize -> Large];
dummydata = Range[7];
(* "invisible" barchart: *)
dummybch = BarChart[dummydata, LabelingFunction -> Below, ChartElements -> Graphics[{Opacity[0], Circle[]}]];
Show[bch, dummybch]

Hi Jonathan,

This does most of want you want, but there are issues with the placement of the values, especially for the zero values. Probably have to use a custom LabelingFunction to fix them.

BarChart[data,
 ChartLayout -> "Stacked",
 Axes -> True,
 Frame -> True,
 FrameLabel -> {"Food Age {days}", "Consumption {calories}"},
 PlotLabel -> "Food Consumption by Age",
 ChartLegends -> {"Fresh kill", "Canned food", "Kitchen scraps", "Dry food"},
 LabelingFunction -> Top]

Hi Henrik,

Nice, +1. Jonathan also wanted each bar to have x-axis labels of 1 to 7. I tried various ChartLabels settings but failed. Do you know how to do that?