According to MIT Election Data and Science Lab's U.S. President Precinct-Level Returns 2016 dataset, there were around 580 such precincts (the precise number is difficult to count as some counties seem to report write-ins, etc as separate precincts). For example:
- Davidson County's 601 precinct in Tennessee gave 1207 votes out of 1277 to Evan McMullin, and none to either Trump or Clinton.
- Larimer County's 2145235206 precinct in Colorado gave 965 votes out of 1111 to Clinton, and most of the rest to Gary Johnson or Jill Stein.
Here is a summary of the precincts where Trump's vote share was less than 1%, though as I said there may be some mistakes due to how certain types of votes are counted.
Donald Trump Hillary Clinton Total Trump %
state county_name precinct
Tennessee Davidson County 601 0 0 1277 0.000000
Rutherford County 50 0 0 481 0.000000
Ohio Cuyahoga County CLEVELAND-02-R 0 419 425 0.000000
Alabama Mobile County THOMAS SULLIVAN COMM CENTER #1 0 280 532 0.000000
Louisiana Pointe Coupee Parish 00 13A 0 390 392 0.000000
St. James Parish 00 07 0 291 292 0.000000
Maryland Baltimore city School No. 35 0 277 281 0.000000
Pennsylvania Philadelphia County 2830 0 349 350 0.000000
Colorado Larimer County 2145235206 0 965 1111 0.000000
Pennsylvania Philadelphia County 3430 0 266 268 0.000000
5890 0 308 312 0.000000
1230 0 277 285 0.000000
2170 0 404 406 0.000000
6230 0 278 280 0.000000
7090 0 282 282 0.000000
Illinois Cook County Ward 20 Precinct 12 0 432 438 0.000000
Ward 09 Precinct 05 0 417 423 0.000000
Ward 24 Precinct 35 0 433 438 0.000000
New Jersey Camden County Pennsauken Twp 0 0 265 0.000000
Alabama Jefferson County 2370 - NEW BETHEL BAPTIS 1 487 946 0.105708
Illinois Cook County Ward 09 Precinct 26 1 663 670 0.149254
Alabama Montgomery County 211 RUFUS LEWIS LIBRARY #2 1 342 620 0.161290
Mobile County THOMAS SULLIVAN COMM CENTER #2 1 288 557 0.179533
Pennsylvania Philadelphia County 11150 1 510 516 0.193798
Illinois Cook County Ward 08 Precinct 36 1 496 514 0.194553
Louisiana Caddo Parish 00 057 1 496 500 0.200000
Illinois Cook County Ward 21 Precinct 09 1 495 499 0.200401
Pennsylvania Philadelphia County 7460 1 484 488 0.204918
Illinois Cook County Ward 17 Precinct 18 1 472 482 0.207469
Pennsylvania Philadelphia County 12120 1 461 467 0.214133
... ... ... ... ...
Alabama Jefferson County 2380 - FIVE POINTS WEST 12 642 1240 0.967742
Michigan Wayne County DETROIT CITY; 373 4 397 412 0.970874
Ohio Cuyahoga County CLEVELAND-09-Q 3 300 308 0.974026
Illinois Cook County Ward 17 Precinct 35 4 398 409 0.977995
Mississippi Hinds County Precinct 11 3 302 306 0.980392
New Jersey Hudson County Jersey City WF D24 5 499 510 0.980392
Missouri St. Louis city W 04 P 06 3 298 306 0.980392
Mississippi Sunflower County Indianola #2 East 15 1496 1529 0.981033
Pennsylvania Philadelphia County 12390 4 395 407 0.982801
11120 5 480 508 0.984252
New York Kings County 061/58 2 211 254 0.787402
Illinois Cook County Ward 21 Precinct 02 4 393 406 0.985222
Wisconsin Milwaukee County CITY OF MILWAUKEE Ward 107 7 691 710 0.985915
Illinois Cook County Ward 37 Precinct 35 5 496 507 0.986193
Ohio Cuyahoga County CLEVELAND-01-F 6 595 608 0.986842
Illinois Cook County Ward 24 Precinct 29 3 298 304 0.986842
Pennsylvania Philadelphia County 6990 3 298 304 0.986842
8720 3 299 304 0.986842
Illinois Cook County Ward 24 Precinct 13 3 293 304 0.986842
Michigan Genesee County FLINT CITY; Ward 1; Precinct 1 9 894 911 0.987925
Illinois Cook County Ward 09 Precinct 43 5 490 506 0.988142
Missouri St. Louis city W 01 P 04 5 494 506 0.988142
Illinois St. Clair County PRECINCT 02 5 496 505 0.990099
Pennsylvania Philadelphia County 2500 4 398 404 0.990099
2210 4 394 403 0.992556
Georgia Chatham County 8-10 Carver Heights Community Center 2 247 251 0.796813
California Alameda County 336100 3 302 352 0.852273
Illinois Cook County Ward 08 Precinct 52 6 591 603 0.995025
Michigan Wayne County DETROIT CITY; 361 6 585 602 0.996678
Alabama Jefferson County 2170 - HEMPHILL SCHOOL R 21 1073 2101 0.999524
[578 rows x 4 columns]