This paper presents an algorithm for nonlinear adaptive control of the viral load in HIV-1 infection. The infection model considered is a reduced complexity nonlinear state-space model with two state variables, that represent the plasma concentration of uninfected and infected CD4+ T-cells of the human immune system. The viral load is assumed to be proportional to the concentration of infected cells. First, a change of variables that exactly linearizes the system is obtained. For the resulting linear system the manipulated variable is obtained by state feedback. To compensate for the uncertainty in the infection parameter of the model an estimator based on a Control Lyapunov Function is designed.