We measure changes in the penetration depth lambda of the T_{c} approximately 6 K superconductor LaFePO. In the process, scanning SQUID susceptometry is demonstrated as a technique for accurately measuring local temperature-dependent changes in lambda, ideal for studying early or difficult-to-grow materials. lambda is found to vary linearly with temperatures from 0.36 to approximately 2 K, with a slope of 143 +/- 15 A/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to approximately T_{c}/3, similar to the cuprate superconductors, indicates well-developed nodes.
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