Chevron routinely runs 30¢ - 50¢ higher than other brands. In my town RG is 50¢ higher while Premium is 30¢ higher. Neither Chevron carries diesel. The Chevron that did carry diesel was torn down a few years back to build a CVS pharmacy.
They do seem to be consistently higher than other brands, but the variance is definitely regional. Down here on the coast they are priced similarly to Shell and Texaco, which are among the costliest places to fill for gas or diesel.
Of the three, Chevron is the "cheapest" but still higher than brands like Dodge's, Murphy USA and Tom Thumb CITGO.
There's only three Chevron stations in my town and two of them carry diesel (one also carries off-road diesel since it's near farms). The one on the main highway has pricey gas, but their diesel is a crapshoot. Sometimes it's 30¢ higher than nearby competitors, sometimes it's 30¢ lower. They don't advertise the price and I don't think it changes unless they get a delivery, which must not be very often. For that reason, I never buy from there, although I have a few times in the past when the price was irresistibly low. The fuel ran fine, but I felt uneasy about taking the risk.
I'm always wary of places that sell diesel but don't advertise a price for it. They can't ever have good turnover.
Despite the fact that we're supposed to be in the thick of winter, I'm happy to say that diesel is still at or just below the price of midgrade at a few stations in my region. The predicted drop in gasoline prices didn't happen (or didn't last long enough to leave an impression) and the predicted rise in diesel was less than previous winters.
It's also nice that the spread for diesel remains, as always, pretty consistent. Here's a check of regional prices in my part of Baldwin County:
RUG: $2.039-2.229 (not including full service)
MID: $2.159-2.629
PRM: $2.449-3.119
D2: $2.259-2.459
Ethanol free Marine/midgrade: $2.669-2.999