We report the discovery of seven new Galactic pulsars with the Canadian Hydrogen Intensity Mapping Experiment's Fast Radio Burst (CHIME/FRB) backend. These sources were first identified via single pulses in CHIME/FRB, then followed up with CHIME/Pulsar. Four sources appear to be rotating radio transients, pulsar-like sources with occasional single-pulse emission with an underlying periodicity. Of those four sources, three have detected periods ranging from 220 ms to 2.726 s. Three sources have more persistent but still intermittent emission and are likely intermittent or nulling pulsars. We have determined phase-coherent timing solutions for the latter two. These seven sources are the first discovery of previously unknown Galactic sources with CHIME/FRB and highlight the potential of fast radio burst detection instruments to search for intermittent Galactic radio sources.