Below is the graph of $y = a \cos bx$ for some positive constants $a$ and $b.$  Find $a.$

[asy]import TrigMacros;

size(400);

real g(real x)
{
	return (3*cos(4*x));
}

draw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);
trig_axes(-3*pi,3*pi,-4,4,pi/2,1);
layer();
rm_trig_labels(-5, 5, 2);

label("$1$", (0,1), E);
label("$2$", (0,2), E);
label("$3$", (0,3), E);
label("$-1$", (0,-1), E);
label("$-2$", (0,-2), E);
label("$-3$", (0,-3), E);
[/asy]
The maximum value of $a \cos bx$ is $a,$ so $a = \boxed{3}.$