In the recent years, HTTP Adaptive Bit Rate (ABR) streaming including Dynamic Adaptive Streaming over HTTP (DASH) has become the most popular technology for video streaming over the Internet. The client device requests segments of content using HTTP, with an ABR algorithm selecting the quality at which to request each segment to trade-off video quality with the avoidance of stalling. This introduces high latency compared to traditional broadcast methods, mostly in the client buffer which needs to hold enough data to absorb any changes in network conditions. Clients employ an ABR algorithm which monitors network conditions and adjusts the quality at which segments are requested to maximise the user's Quality of Experience. The size of the client buffer depends on the ABR algorithm's capability to respond to changes in network conditions in a timely manner, hence, low latency live streaming requires an ABR algorithm that can perform well with a small client buffer. In this paper, we present Llama - a new ABR algorithm specifically designed to operate in such scenarios. Our new ABR algorithm employs the novel idea of using two independent throughput measurements made over different timescales. We have evaluated Llama by comparing it against four popular ABR algorithms in terms of multiple QoE metrics, across multiple client settings, and in various network scenarios based on CDN logs of a commercial live TV service. Llama outperforms other ABR algorithms, improving the P.1203 Mean Opinion Score (MOS) as well as reducing rebuffering by 33% when using DASH, and 68% with CMAF in the lowest latency scenario.