Like Jerry said, it is probably the auxiliary air compressor for the leveling system. Mine is in the rear, but may be the same system. Mine is the HWH system. My compressor went bad and I found the identical compressor at Zoro.com Zoro Tools. They also had a rebuild kit for several small compressors like that. The one I purchased was the exact model number as the one I replaced.
Your leveling system checks periodically to see if it is level, and if not, it will relevel and the little compressor supplies air for that process. On mine, I believe it is supposed to check every 30 minutes or so. If you can remove the compressor and do a search for the brand and model number, it should be easy to locate. As another possibility, Monaco Coach will have one for you, but probably at a higher price. Hope this may help, Happy Trails Bert
2006 Monaco Dynasty Diamond IV 42' Tag, ISL 400,(new to us), Residential Refrig, 10KW Onan, Bosch Washer/220V Dryer (previously 2003 American Tradition 40W) 2010 Chev Malibu LT