Worldcon (World Science Fiction Convention) is in Chengdu, China in October this year. Is a visa required, and (if so) is it possible to get one if you are a United Statesian?
Yes, an American needs a visa to visit mainland China, however, you don’t need a visa to visit Taiwan.
Unless they’ve changed things in the past 5 years, you do need a Visa to visit China yes. Being a US citizen is not a bar to getting one.
Yeah, my previous passport is chock full of Chinese visas. I think the most serious requirement to get one is the part where they charge you the fee.
Note that if you go with a single-entry visa, be careful of your itinerary. They really mean it; it’s one-time use. I often would fly into Hong Kong, and once when I only had a single-entry approved, I crossed the border into Shenzhen and then realized I couldn’t go back to Hong Kong for the weekend as I had hoped since I already used my one shot.
Was this back when Hong Kong’s lease was still running, or does a “special economic zone” count as not-China?
We visited China about 10 years ago. The process then was rather cumbersome - if I recall, we had to send our passports to a travel agency near the Chinese embassy, who then walked them through the visa process. The application seemed to center on things like “are you an employee of a media company or the government?” more than other details.
Things might be a bit more complicated in the current political climate, but generally it wasn’t too bad. Customs was more of a formality, but then we went via Hong Kong. (Even after the repatriation - HK was a separate no-visa-required area, hence the entry checks leaving the territory for the rest of China) The important thing at the time was whether you needed a re-entry visa. The warning was that Hong Kong being a special zone at the time with no visa requirement, going in and out of neighbouring Chinese areas would require a multiple-entry visa. (Also, Tibet required a separate additional entry permit and a guide company to arrange your tour).
Chengdu being in the middle of China, I suspect you won’t need more than single entry unless you plan a very unusual itinerary. It’s an amazing country with millennia of history that we in the west hear very little about.
This was through 2008 or so. Entry into Hong Kong and entry into China proper are still two different things today, if my google skills hold up.
Yes, this was the case in 2010 too - as I understood, we could have taken the ferry from HK to Macau and back and forth, no visa needed, but entry from either into the rest of China counted as an entry; so unless you had a multiple-entry visa, you could only do that once. This was a warning for tourists - if your itinerary takes you further on into the rest of China, you won’t be able to, if you burn up that one entry with a short day trip to the area neighbouring HK (ie. Shenzhen).
(Google earth shows me there’s a bridge HK to Macau now???)
For visa and immigration purposes, Hong Kong still works, effectively, as if it were a separate country; there are border checks between HK and Shenzhen, and Westerners usually have visa-free travel to HK but not mainland China. Shenzhen is mainland China but a special economic zone, which means there are facilitated routes to get a visa that’s limited to Shenzhen. But it’s not part of HK, neither administratively nor for immigration purposes.
The plan is to go to Chengdu only, not Hong Kong or Taiwan.
I think the cost for multiple entries is the same as for single entry if you are a US or Canadian citizen.
Short answer, yes US citizens need a visa to enter China.
There are multiple flavors of visa’s such as single entry, double entry, multiple entry.
Cost for visa’s are tit-for-tat. Whatever the US charges for a comprable visa, is what China charges and vice versa.
Yes, US private citizens are welcome to come spend gringo dollars in country. 
A visa is needed. There is a fee, and a delay in obtaining it. I think you may need to report flight in and out of the country (but maybe not - might be thinking of somewhere else or might no longer be the case).
If you (OP) live near a Chinese embassy then I recommend going there early in the morning and standing in line. I traveled twice to Shanghai for work, and fortunately I’m within an hour of the embassy in San Francisco. So I just drove up there and waited in line.
A couple hours later I had it in hand
Minor nitpick here (but one that might help the OP in locating where to go): A country always has only one embassy to another country, usually in the capital. Other offices, such as the Chinese office in San Francisco, are consulates (but consulates can issue visas - in fact, visa issuance is a consular matter even when carried out by an embassy).
It’s also possible that the embassy or consulate outsources part of the processing of a visa application to an external service supplier. When I applied for a visa to mainland China a few years ago, I did not go to the Chinese consulate in my city, but to a “visa application service centre” located in a different building. (The visa was, however, issued by the consulate, which has excusive power to do this.)
This was my impression for Canadian applications back around 2010 - there was one agency that handled all the visa applications, as far as I could tell, and walked your passport across the street to the embassy in Ottawa. It was relatively painless, I was simply without my passport for a week or two. The only concern was IIRC that you need to book the flight first, they wanted your itinerary for the application. But, back then at least, there was no difficulty getting there, and no harassment or difficulty travelling around. We wandered several big cities by ourselves.