Machine-learning algorithms are improving and automating important functions in medicine, transportation, and business. Government officials have also started to take notice of the accuracy and speed that such algorithms provide, increasingly relying on them to aid with consequential public-sector functions, including tax administration, regulatory oversight, and benefits administration. Despite machine-learning algorithms’ superior predictive power over conventional analytic tools, algorithmic forecasts are difficult to understand and explain. Machine learning’s “black-box” nature has thus raised concern: Can algorithmic governance be squared with legal principles of governmental transparency? We analyze this question and conclude that machine-learning algorithms’ relative inscrutability does not pose a legal barrier to their responsible use by governmental authorities. We distinguish between principles of “fishbowl transparency” and “reasoned transparency,” explaining how both are implicated by algorithmic governance but also showing that neither conception compels anything close to total transparency. Although machine learning’s black-box features distinctively implicate notions of reasoned transparency, legal demands for reason-giving can be satisfied by explaining an algorithm’s purpose, design, and basic functioning. Furthermore, new technical advances will only make machine-learning algorithms increasingly more explainable. Algorithmic governance can meet both legal and public demands for transparency while still enhancing accuracy, efficiency, and even potentially legitimacy in government.