Processing latency is a critical issue for active noise control (ANC) due to the causality constraint of ANC systems. This paper addresses low-latency ANC in the context of deep learning (i.e. deep ANC). A time-domain method using an attentive recurrent network (ARN) is employed to perform deep ANC with smaller frame sizes, thus reducing algorithmic latency of deep ANC. In addition, we introduce a delay-compensated training to perform ANC using predicted noise for several milliseconds. Moreover, a revised overlap-add method is utilized during signal resynthesis to avoid the latency introduced due to overlaps between neighboring time frames. Experimental results show the effectiveness of the proposed strategies for achieving low-latency deep ANC. Combining the proposed strategies is capable of yielding zero, even negative, algorithmic latency without affecting ANC performance much, thus alleviating the causality constraint in ANC design.