If an airline passenger is refused admission to the the destination country or a transit airport country, the airline is subject to fines and is required to return the passenger to the airport of departure at the airlines' cost (although the airline may try to collect that money from the passenger). Thus, airlines are very careful to check passengers' documentation before letting them board the flight.
Airlines use the Timatic database to make this check. Here's a link to the database; there are others. Entering your information (Indian nationality, destination Chile) into the link yields this text:
Chile - Destination Passport
Document validity rules:
Passports and other documents accepted for entry must be valid on arrival.
So you must carry your passport, and it must be valid upon your arrival in Chile.
The Timatic text goes on to say:
Chile - Destination Visa
The following are exempt from holding a visa:
Nationals of India with a visa issued by the USA valid for a minimum of 6 months from the arrival date. This does not apply to "C" visas.. They must travel as tourists for a maximum stay of 90 days.
Visitors of Easter Island are allowed to stay for a maximum of 30 days. They must :
- have a return ticket, and
- submit an entry form on https://ingresorapanui.interior.gob.cl, and
- have a reservation in a hotel approved by Sernatur (http://serviciosturisticos.sernatur.cl/alojamientos/rapanui), or
- have an invitation letter from a resident of Easter Island.
Visitors not holding return/onward tickets could be refused entry.
If your US H-1 Visa is good for at least six months from your date of arrival in Chile, you do not need an additional visa. You should carry as well proof of a return or onward ticket.
Note, however, the special requirements if you wish to vist Easter Island.
Finally: this answer assumes a non-stop flight from the US to Chile. If your flight stops somewhere else as a layover or transit, you will need to disclose that information to Timatic to see if a visa or visas are required for any additional stop or stops.
EDIT 1: I think the above answer is incomplete, and comes to the wrong conlcusion. @Traveller has pointed out (see his comment below) that if the airline employee believes the OP is a a US resident and enters "Resident of US" into Timatic, the result displayed is this:
Visa required, except for Nationals of India with a Permanent
Resident/Resident Alien Card (Form I-551) issued by the USA
for a maximum stay of 90 days.
The OP has a US visa, but does not have a Green Card (Permanent Resident Card). Thus, if this result is displayed, the OP could be denied boarding.
It is not clear if a foreign-passport holder who's living in the US after having entered on a visa becomes a US resident for purposes of subsequent international air travel. I would not like to have my trip to South America derailed because an airline employee and I disagreed about semantics.
I'll change my answer: the OP should obtain a Chilean visa for his trip.
EDIT 2: the OP has cited this Chilean government document, which contains this text:
The Consular Section of the Embassy of Chile in India states that henceforth all Indian travellers holding a valid US Visa, with current validity of six months, do not require a Chilean tourist visa (either Simple Tourism or Multiple Tourism or Multiple-Business). This came into effect from the 1st April 2019.
- All travellers to Chile need to have a valid passport for at least six months from the date of entrance into the country.
- Tourist travellers should have enough financial support for their stay in Chile.
- The period of stay in Chile for tourists is up to 90 days.
- Not applicable to USA Transit Visa (Visa C).
This document is clear that the OP does not require a Chilean visa.
Still, I'd worry a bit that airline check-in staff might see what's presented by Timatic and conclude differently. Asking for a supervisor would then be in order.
All in all: I think now that the OP does not require a Chilean visa for tourist purposes. A conservative approach, however, would be to obtain a Chilean visa to eliminate the difficulties that might arise over a different conclusion drawn because of the imprecision of Timatic's use of the concept "residency."