HIV viral dynamics studies involve repeated measurement of viral load in HIV-infected individuals, to asses short-term rates of viral load change in response to interventions such as initiation or withdrawal of antiviral therapy. Such studies are an important source of information on HIV pathogenesis. This paper concerns some statistical issues arising in their design. Using a linear random-effects model to incorporate between-patient differences in rates of viral load change, I discuss the choice of number of individuals and frequency of observation per individual. I suggest an approach for calculating the optimal sample size and observation frequency, based on minimizing the total number of viral load measurements that one needs to undertake. The conclusion, using this approach, is that over a period of linear change in viral load, three to five measurements per individual is generally appropriate. I also examine the observation frequency when the number of available individuals is limited, in which case it is shown that one can use a higher frequency of measurement per individual to achieve adequate power or precision. Finally, I consider sources of data for prior specification of variance components, together with conservative designs that are insensitive to a lack of prior information about between-patient differences.