Exactly, the answer comes from the lift equation:
L = CL * A * Rho/2 * V^2
Assuming weight is constant, the lift for straight and level flight must equal weight (L = W). The higher the altitude, the lower the density (Rho) of the air (mainly due to reduced air pressure). And if density decreases, you have to increase true airspeed (V) in order to create the same amount of lift and keep forces balanced.