Searching for gravitational waves (GWs) from binary black holes (BBHs) with LIGO and Virgo involves matched-filtering data against a set of representative signal waveforms—a template bank—chosen to cover the full signal space of interest with as few template waveforms as possible. Although the component black holes may have significant angular momenta (spin), previous searches for BBHs have filtered LIGO and Virgo data using only waveforms where both component spins are zero. This leads to a loss of signal-to-noise ratio for signals where this is not the case. Combining the best available template placement techniques and waveform models, we construct a template bank of GW signals from BBHs with component spins χ1,2∈[−0.99,0.99] aligned with the orbital angular momentum, component masses m1,2∈[2,48]M⊙, and total mass Mtotal≤50 M⊙. Using effective-one-body waveforms with spin effects, we show that less than 3% of the maximum signal-to-noise ratio (SNR) of these signals is lost due to the discreetness of the bank, using the early Advanced LIGO noise curve. We use simulated Advanced LIGO noise to compare the sensitivity of this bank to a nonspinning bank covering the same parameter space. In doing so, we consider the competing effects between improved SNR and signal-based vetoes and the increase in the rate of false alarms of the aligned-spin bank due to covering a larger parameter space. We find that the aligned-spin bank can be a factor of 1.3–5 more sensitive than a nonspinning bank to BBHs with dimensionless spins >+0.6and component masses ≳20 M⊙. Even larger gains are obtained for systems with equally high spins but smaller component masses.