Spectral decomposition of variations in heart rate permits noninvasive measurement of autonomic nervous activity in humans and animals. Autonomic metrics based on spectral analysis are useful in monitoring clinical conditions such as diabetic neuropathy and reinnervation in heart transplant patients. A persistent problem in deriving such autonomic measures is the prerequisite of an accurate and unbiased power spectrum of heart rate variability (HRV). Numerous parametric and nonparametric power spectrum estimators have been introduced, each with its own advantages and drawbacks. Estimator bias has received little attention, despite the fact that at least one common HRV spectrum estimator, the autoregressive method, is known to exhibit bias even in idealized circumstances. We introduce an approximately minimum bias, nonparametric, multichannel spectrum estimation procedure for HRV and contemporaneous signals. The procedure, which is designed specifically for irregular sampling, does not require data segmentation and provides statistically consistent, low variance multichannel spectrum estimates. Estimator performance on simulated and clinical data is presented and compared with results from autoregressive models and Welch periodograms with and without compensation for irregular sampling. Results indicate that the proposed method exhibits advantages over conventional HRV spectrum estimators. Relative computational complexity of the proposed method is also considered.