It is known that secret keys can be extracted from some USIM cards using Correlation Power Analysis (CPA). In this paper, we demonstrate a more advanced attack on USIMs, based on deep learning. We show that a Convolutional Neural Network (CNN) trained on one USIM can recover the key from another USIM using at most 20 traces (four traces on average). Previous CPA attacks on USIM cards required high-quality oscilloscopes for power trace acquisition, an order of magnitude more traces from the victim card, and expert-level skills from the attacker. Now the attack can be mounted with a $1000 budget and basic skills in side-channel analysis.