Blooms as in the following pic mid-July Has never borne any fruit/nut. Not a big tree considering it is about 65 years old, maybe 25 feet tall . I'm pretty sure I was told they were a nut tree but I could be misremembering. Likely not native to the state of Massachusetts but I don't know that for sure either.
Leaves remind me of chestnut. The blossoms maybe . If no others are around that may be why the lack of nuts.
Sometimes a scale reference is helpful. ... and, trunk at chest height: It is also possible that they are male/female trees like holly but only have seed pods like honey locust. There is a pair planted about 10 feet apart but one died in the drought a couple of Summers ago.
Chinese chestnut sounds right and not being self-pollinating would explain the two planted together. I know they were planted because my father planted them. He's not around any more to ask. I looked up chinese chestnut once a long time ago and the leaves didn't look right but there must be a bunch of cultivars with some looking more like american chestnut leaves.
