Parallel channels form a basic building block for communication systems, including those based on OFDM and CDMA. While parallel Gaussian noise channels have been widely studied, parallel impulsive noise channels have received significantly less attention despite their importance in a range of modern communication systems. In this paper, this problem is addressed and a power allocation strategy is developed for parallel symmetric α-stable noise channels-a key class of impulsive noise channels. We show that our strategy can improve achievable rates by up to a factor of 1.5 over the standard waterfilling algorithm that assumes the noise is Gaussian.